{ "model": { "rank": 9027, "code": "thing-q176737", "model_id": "vr.tr.stochastic-process", "name": "stochastic process", "purpose": "Let an agent explain stochastic processes by type, properties, simulation and applications in science, engineering, finance and machine learning.", "family": "Thing Registry", "category": "Cross-cutting context", "status": "research-draft", "kind": "thing", "plane": "XCT", "domain": "XCT.QLT", "industry": "", "version": "", "url": "/models/thing/q176737/", "tier": 2, "score": 49, "payload": { "layer": "wikidata", "aliases": [ "stable process", "Cauchy process", "Markov renewal process", "counting process", "stationary process", "Gaussian process", "discrete-time stochastic process", "Poisson clumping", "local martingale", "urban scaling", "Markov process", "Indian buffet process", "sample path", "Affiner Prozess", "local time", "Predictable process", "jump process", "thermal fluctuations", "Branching process", "Chinese restaurant process", "Adapted process", "semimartingale", "continuous-time stochastic process", "continuous stochastic process", "diffusion process", "Dirichlet process", "martingale", "Feller-continuous process", "hierarchical Dirichlet process", "Brownian bridge", "Jump diffusion", "Lindley equation", "Markov model", "point process", "regenerative process", "sample-continuous process", "Simon model", "Superprocess", "random walk", "random graph" ], "aliasCount": 61, "merged": 61, "knownIn": 49, "facets": null, "markers": [], "lexicalClass": "", "senseRank": null, "alsoRegisteredAs": null, "source": { "dataset": "wikidata", "item": "Q176737", "url": "https://www.wikidata.org/wiki/Q176737", "license": "CC0 1.0" } }, "research": { "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-11T12:12:49Z", "providers": [ "Claude" ], "breadth": "written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify", "pass": 2, "wave": 1, "engine": "claude" }, "metaModel": { "id": "THING-Q176737", "registryId": "vr.tr.stochastic-process", "name": "stochastic process", "version": "0.2.0-wave.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "XCT.QLT" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q176737/", "model": { "registry_id": "vr.tr.stochastic-process", "name": "stochastic process", "purpose": "Let an agent explain stochastic processes by type, properties, simulation and applications in science, engineering, finance and machine learning.", "definition": "A collection of random variables indexed by time or space that models systems evolving with randomness, such as Markov chains, Poisson processes, Brownian motion (the Wiener process), Gaussian processes and random walks.", "what_it_is_for": "Modelling random phenomena over time or space.", "affordances": [ "identify a suitable process type", "explain properties such as stationarity and the Markov property", "simulate sample paths", "apply processes in modelling" ], "distinguishing_features": [ "Indexed family of random variables", "Discrete or continuous time", "Characterised by distributions and dependence", "Widely applied" ], "appearance": "Not physical; shown as random sample paths, transition diagrams and equations.", "visual_identification": [ "Jagged sample paths", "Transition matrices", "A deterministic process has no randomness" ], "physical_properties": [], "families_and_kinds": [ "Markov chains and processes", "Poisson and counting processes", "Brownian motion and diffusions", "Gaussian processes", "stationary and renewal processes" ], "related_models": [ { "relation": "is a kind of", "target": "mathematical object", "why": "category" }, { "relation": "is studied in", "target": "probability theory", "why": "field" }, { "relation": "includes", "target": "Markov chain", "why": "example" }, { "relation": "is used in", "target": "queueing theory and finance", "why": "applications" } ], "identifiers": [], "standards_and_regulation": [ "No specific regulation; model risk guidance applies in finance" ], "failure_modes_and_hazards": [ "Assuming stationarity without checking", "Misapplying models to real risks" ], "in_scope": [], "out_of_scope": [], "characteristics": [] }, "sources": [], "structure": { "bundles": [ { "id": "types", "name": "Types", "description": "Which process.", "rationale": "Types have properties.", "layers": [ { "id": "choose", "name": "Choose", "description": "Model choice.", "findings": [ { "id": "choose-finding", "name": "Choose", "description": "Model choice.", "questions": [ { "text": "Which process type fits this phenomenon?", "kind": "definition" }, { "text": "What assumptions does it make?", "kind": "boundary" } ] } ] }, { "id": "properties", "name": "Properties", "description": "Markov and stationarity.", "findings": [ { "id": "properties-finding", "name": "Properties", "description": "Properties.", "questions": [ { "text": "Does the process have the Markov property or stationarity?", "kind": "definition" }, { "text": "How can that be tested?", "kind": "measurement" } ] } ] } ] }, { "id": "mathematics", "name": "Mathematics", "description": "Theory.", "rationale": "Theory underpins use.", "layers": [ { "id": "distributions", "name": "Distributions", "description": "Finite-dimensional distributions.", "findings": [ { "id": "distributions-finding", "name": "Distributions", "description": "Distributions.", "questions": [ { "text": "What are the mean and covariance functions?", "kind": "measurement" }, { "text": "How are they estimated?", "kind": "measurement" } ] } ] }, { "id": "calculus", "name": "Calculus", "description": "Stochastic calculus.", "findings": [ { "id": "calculus-finding", "name": "Calculus", "description": "Stochastic calculus.", "questions": [ { "text": "How does Ito calculus handle Brownian motion?", "kind": "definition" }, { "text": "Which textbook explains it?", "kind": "provenance" } ] } ] } ] }, { "id": "simulation", "name": "Simulation", "description": "Computation.", "rationale": "Simulation reveals behaviour.", "layers": [ { "id": "paths", "name": "Paths", "description": "Sample paths.", "findings": [ { "id": "paths-finding", "name": "Paths", "description": "Sample paths.", "questions": [ { "text": "How can sample paths be simulated for this process?", "kind": "action" }, { "text": "Which libraries help?", "kind": "provenance" } ] } ] }, { "id": "fitting", "name": "Fitting", "description": "Estimation.", "findings": [ { "id": "fitting-finding", "name": "Fitting", "description": "Fitting.", "questions": [ { "text": "How are parameters estimated from data?", "kind": "measurement" }, { "text": "How is fit checked?", "kind": "boundary" } ] } ] } ] }, { "id": "applications", "name": "Applications", "description": "Uses.", "rationale": "Uses span fields.", "layers": [ { "id": "fields", "name": "Fields", "description": "Domains.", "findings": [ { "id": "fields-finding", "name": "Fields", "description": "Application fields.", "questions": [ { "text": "How are stochastic processes used in queueing, biology or signal processing?", "kind": "definition" }, { "text": "Which examples are classic?", "kind": "provenance" } ] } ] }, { "id": "finance", "name": "Finance", "description": "Models.", "findings": [ { "id": "finance-finding", "name": "Finance", "description": "Financial models.", "questions": [ { "text": "How are these processes used in financial models, in general terms?", "kind": "definition" }, { "text": "Is the user seeking personal investment advice?", "kind": "boundary" } ] } ] } ] } ] }, "openQuestions": [ "Should each process type be a separate entry?", "How should simulation tools be linked?", "How should applications be linked?" ], "statistics": { "bundles": 4, "layers": 8, "findings": 8, "questions": 16 } }, "draft": { "generator": "vr.draft.v3", "status": "draft-generated", "researched": false, "archetype": "abstract concept", "method": "Written from the archetype playbook - what this kind of thing needs beyond identity and provenance - and from the structure that recurred across 6,333 models already researched by two engines. Applied to this entry by rule. No source was read for this thing and no claim here is researched. This entry carries no facets of its own, so they were inferred from its domain - a guess about a whole domain applied to one thing.", "facetsInferred": true, "nextPass": "A researcher replaces this draft with a sourced specification. Treat every sentence below as a proposal to argue with.", "purpose": "Give an agent a durable, checkable way to recognise a stochastic process, record what state it is in, and decide what may be done with it.", "whatItIs": "Let an agent explain stochastic processes by type, properties, simulation and applications in science, engineering, finance and machine learning.", "characteristics": { "substance": "abstract", "origin": "conceptual", "agency": "inert" }, "whatYouCanDoWithIt": [ "observed and measured" ], "distinguishingFeatures": [ "Names folded into this entry, which a task may need to split apart again: stable process, Cauchy process, Markov renewal process, counting process, stationary process, Gaussian process, discrete-time stochastic process, Poisson clumping, local martingale, urban scaling, Markov process, Indian buffet process.", "61 finer distinctions are held as aliases rather than separate entries, because telling them apart needs a task that asks for it.", "Described in 49 Wikipedia languages, which is a measure of how widely the thing is known, not of how important it is." ], "openQuestionsForResearch": [ "Which of the bundles below does a real task actually need, and which are ceremony?", "What does this thing have that the facets do not capture at all?", "Which neighbouring kind is most often confused with a stochastic process, and on what evidence are they told apart?" ], "whatItIsMadeOf": "an abstraction with no physical instance", "physicalCharacter": [ "Does nothing on its own; everything it does, something else did to it.", "These come from the domain this entry sits in rather than from the entry itself, so treat them as a first guess about the whole domain applied to one thing." ], "whatCanBeDoneWithIt": [ "observe it, measure it, record its state" ], "howItIsRecognised": [ "Nothing to see. What is recognised is an instance of it, and which instances count is exactly what is argued about." ], "relatedModels": [ { "relation": "covers", "note": "Finer kinds folded into this entry because telling them apart needs a task that asks for it. Each is a model waiting to be split out when one does.", "targets": [ "stable process", "Cauchy process", "Markov renewal process", "counting process", "stationary process", "Gaussian process", "discrete-time stochastic process", "Poisson clumping", "local martingale", "urban scaling", "Markov process", "Indian buffet process" ] } ], "standing": "Described in 49 Wikipedia languages, which measures how widely it is written about rather than how important or how common it is. 61 finer distinctions are held inside this entry as names rather than as separate models.", "structure": { "bundles": [ { "id": "identity-and-classification", "name": "Identity, naming and classification", "description": "How an agent tells one stochastic process from another, and a stochastic process from things that resemble it.", "rationale": "Recognition comes before every other claim. Without stable identity nothing else in the model can be trusted to be about the same thing twice.", "layers": [ { "id": "naming-and-identifiers", "name": "Names and identifiers", "description": "The names this thing goes by and the identifiers that survive translation and time.", "findings": [ { "id": "preferred-name-and-aliases", "name": "Preferred name, aliases and local names", "description": "Which name to use, which names mean the same thing, and which merely sound similar.", "questions": [ { "id": "preferred-name-and-aliases-q01", "text": "What identifies and describes the name of a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "preferred-name-and-aliases-q02", "text": "Who or what asserted this about the name of a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "preferred-name-and-aliases-q03", "text": "What may an agent decide or do once the name of a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "stable-identifiers", "name": "Stable identifiers and external keys", "description": "Identifiers that keep pointing at this kind of thing across systems and languages.", "questions": [ { "id": "stable-identifiers-q01", "text": "What identifies and describes an identifier for a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stable-identifiers-q02", "text": "Who or what asserted this about an identifier for a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stable-identifiers-q03", "text": "What may an agent decide or do once an identifier for a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "classification-and-granularity", "name": "Classification and granularity", "description": "Where a stochastic process sits among kinds, and how finely a task needs to cut it.", "findings": [ { "id": "kind-and-parents", "name": "Kind, parents and neighbouring kinds", "description": "The classes this thing belongs to and the ones it is next to.", "questions": [ { "id": "kind-and-parents-q01", "text": "What identifies and describes the kind of a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "kind-and-parents-q02", "text": "Who or what asserted this about the kind of a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "kind-and-parents-q03", "text": "What may an agent decide or do once the kind of a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] }, { "id": "distinguishing-features", "name": "Distinguishing features", "description": "What separates a stochastic process from the things most often confused with it.", "questions": [ { "id": "distinguishing-features-q01", "text": "What identifies and describes what distinguishes a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "distinguishing-features-q02", "text": "Who or what asserted this about what distinguishes a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "distinguishing-features-q03", "text": "What may an agent decide or do once what distinguishes a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "state-and-lifecycle", "name": "State and lifecycle", "description": "The states a stochastic process passes through and the events that move it between them.", "rationale": "Most decisions about a thing depend on what state it is in now, which is a claim with a time on it, not a property.", "layers": [ { "id": "lifecycle-stages", "name": "Lifecycle stages", "description": "From coming into existence to ceasing to be one of these.", "findings": [ { "id": "stages-and-transitions", "name": "Stages and transitions", "description": "The stages worth naming and what moves a stochastic process between them.", "questions": [ { "id": "stages-and-transitions-q01", "text": "What identifies and describes the lifecycle of a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "stages-and-transitions-q02", "text": "Who or what asserted this about the lifecycle of a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "stages-and-transitions-q03", "text": "What may an agent decide or do once the lifecycle of a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "observations-and-status", "name": "Observations and current status", "description": "What is observed about a stochastic process, how often and by whom.", "findings": [ { "id": "observation-record", "name": "Observation record", "description": "How an observation of a stochastic process is recorded so that it can be superseded rather than overwritten.", "questions": [ { "id": "observation-record-q01", "text": "What identifies and describes an observation of a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "observation-record-q02", "text": "Who or what asserted this about an observation of a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "observation-record-q03", "text": "What may an agent decide or do once an observation of a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] }, { "id": "definitions-in-contest", "name": "Definitions and who holds them", "description": "What stochastic process is taken to mean, and by whom.", "rationale": "When a field disagrees about a concept, the disagreement is the content. A model that picks one definition silently destroys the information.", "layers": [ { "id": "competing-definitions", "name": "Competing definitions", "description": "The main readings and the traditions behind them.", "findings": [ { "id": "definition-map", "name": "Definitions and their holders", "description": "Each definition with the school or body that holds it.", "questions": [ { "id": "definition-map-q01", "text": "Which definitions of stochastic process are in use, and which tradition or body holds each?", "kind": "definition" }, { "id": "definition-map-q02", "text": "What turns on the difference between them in practice?", "kind": "boundary" } ] } ] }, { "id": "operationalisation", "name": "Operationalisation", "description": "How it is measured or applied when it has to be.", "findings": [ { "id": "operational-record", "name": "Measures and proxies", "description": "Instruments and indicators used to stand in for it.", "questions": [ { "id": "operational-record-q01", "text": "How is stochastic process operationalised or measured in practice, and by what instrument?", "kind": "measurement" }, { "id": "operational-record-q02", "text": "What does that operationalisation leave out, and when does that matter?", "kind": "boundary" } ] } ] } ] }, { "id": "instances-and-use", "name": "Instances, use and consequence", "description": "What counts as an instance of stochastic process and what follows from calling something that.", "rationale": "Applying a concept is an act with consequences, so a model must say what the label licenses and what it does not.", "layers": [ { "id": "instances", "name": "What counts as an instance", "description": "Clear cases, borderline cases and non-cases.", "findings": [ { "id": "instance-tests", "name": "Tests for an instance", "description": "What would settle whether something falls under it.", "questions": [ { "id": "instance-tests-q01", "text": "What would settle whether something is an instance of stochastic process?", "kind": "boundary" }, { "id": "instance-tests-q02", "text": "Which borderline cases are argued about, and on what grounds?", "kind": "definition" } ] } ] }, { "id": "consequence", "name": "Consequence of application", "description": "Rights, duties or decisions that follow from the label.", "findings": [ { "id": "consequence-record", "name": "What the label licenses", "description": "What an agent may do once something is classified this way.", "questions": [ { "id": "consequence-record-q01", "text": "What follows practically once something is treated as stochastic process?", "kind": "action" }, { "id": "consequence-record-q02", "text": "What must an agent not infer from the label alone?", "kind": "action" } ] } ] } ] }, { "id": "provenance-and-evidence", "name": "Provenance, evidence and time", "description": "Where every claim about a stochastic process came from and when it held.", "rationale": "A claim without a source and a time cannot be superseded, only overwritten, and an agent that overwrites loses the ability to explain itself.", "layers": [ { "id": "source-and-authority", "name": "Source and authority", "description": "Who said it, on what evidence, and how strongly.", "findings": [ { "id": "claim-provenance", "name": "Claim provenance and confidence", "description": "The authority behind each claim about a stochastic process and how confident it is.", "questions": [ { "id": "claim-provenance-q01", "text": "What identifies and describes a claim about a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "claim-provenance-q02", "text": "Who or what asserted this about a claim about a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "claim-provenance-q03", "text": "What may an agent decide or do once a claim about a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] }, { "id": "time-and-versions", "name": "Time, versions and supersession", "description": "When a claim was true, when it was learnt, and what replaced it.", "findings": [ { "id": "validity-and-supersession", "name": "Validity period and supersession", "description": "How an old claim about a stochastic process is retired without being erased.", "questions": [ { "id": "validity-and-supersession-q01", "text": "What identifies and describes the validity of a claim about a stochastic process, and in what units or vocabulary?", "kind": "definition", "answer_data": [ "identifiers", "types and classes", "values with units", "explicit unknowns" ] }, { "id": "validity-and-supersession-q02", "text": "Who or what asserted this about the validity of a claim about a stochastic process, by which method, and when was it true?", "kind": "provenance", "answer_data": [ "authority", "method", "evidence", "event time", "knowledge time" ] }, { "id": "validity-and-supersession-q03", "text": "What may an agent decide or do once the validity of a claim about a stochastic process is known, and what must it refuse?", "kind": "action", "answer_data": [ "permitted actions", "preconditions", "refusals", "escalation" ] } ] } ] } ] } ] }, "statistics": { "bundles": 5, "layers": 10, "findings": 12, "questions": 32 } } } }