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Research draft

stochastic process

vr.tr.stochastic-process · XCT.QLT

Let an agent explain stochastic processes by type, properties, simulation and applications in science, engineering, finance and machine learning.

Thing Registry Cross-cutting context

Research draft, second pass

A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.

written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify

Researched by: Claude

Purpose and description

Let an agent explain stochastic processes by type, properties, simulation and applications in science, engineering, finance and machine learning.

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.

It can be 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

What it looks like

Not physical; shown as random sample paths, transition diagrams and equations.

How it is recognised

Jagged sample paths

Transition matrices

A deterministic process has no randomness

Related models

is a kind of - category

mathematical object

is studied in - field

probability theory

includes - example

Markov chain

is used in - applications

queueing theory and finance

In practice

Families and kinds

Markov chains and processes

Poisson and counting processes

Brownian motion and diffusions

Gaussian processes

stationary and renewal processes

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

Also called

stable processCauchy processMarkov renewal processcounting processstationary processGaussian processdiscrete-time stochastic processPoisson clumpinglocal martingaleurban scalingMarkov processIndian buffet processsample pathAffiner Prozesslocal timePredictable processjump processthermal fluctuationsBranching processChinese restaurant processAdapted processsemimartingalecontinuous-time stochastic processcontinuous stochastic processdiffusion processDirichlet processmartingaleFeller-continuous processhierarchical Dirichlet processBrownian bridgeJump diffusionLindley equationMarkov modelpoint processregenerative processsample-continuous processSimon modelSuperprocessrandom walkrandom graph

+21

Where this came from

wikidata · CC0 1.0

Source repository Registry entry point

Drafted structure

Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.

Types Which process.

Types have properties.

Choose

Model choice.

Choose

Model choice.

  1. Which process type fits this phenomenon? definition
  2. What assumptions does it make? boundary

Properties

Markov and stationarity.

Properties

Properties.

  1. Does the process have the Markov property or stationarity? definition
  2. How can that be tested? measurement
Mathematics Theory.

Theory underpins use.

Distributions

Finite-dimensional distributions.

Distributions

Distributions.

  1. What are the mean and covariance functions? measurement
  2. How are they estimated? measurement

Calculus

Stochastic calculus.

Calculus

Stochastic calculus.

  1. How does Ito calculus handle Brownian motion? definition
  2. Which textbook explains it? provenance
Simulation Computation.

Simulation reveals behaviour.

Paths

Sample paths.

Paths

Sample paths.

  1. How can sample paths be simulated for this process? action
  2. Which libraries help? provenance

Fitting

Estimation.

Fitting

Fitting.

  1. How are parameters estimated from data? measurement
  2. How is fit checked? boundary
Applications Uses.

Uses span fields.

Fields

Domains.

Fields

Application fields.

  1. How are stochastic processes used in queueing, biology or signal processing? definition
  2. Which examples are classic? provenance

Finance

Models.

Finance

Financial models.

  1. How are these processes used in financial models, in general terms? definition
  2. Is the user seeking personal investment advice? boundary

What the second pass must settle

  • Should each process type be a separate entry?
  • How should simulation tools be linked?
  • How should applications be linked?
Draft as JSON