Markov processes

E48274

mathematical concept stochastic process

Markov processes are stochastic processes in which the future evolution depends only on the present state and not on the past history.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (11)

Label	Occurrences
Markov processes canonical	10
Markov chains	7
Markov property	7
Markov chain	5
Markov chain theory	2
DTMC	1
Gaussian Markov process	1
Markov decision processes	1
Markov jump process	1
Markov process	1
Markov process theory	1

Statements (50)

Predicate	Object
instanceOf	mathematical concept ⓘ stochastic process ⓘ
canBe	time-homogeneous ⓘ time-inhomogeneous ⓘ
canHave	continuous state space ⓘ countable state space ⓘ discrete state space ⓘ finite state space ⓘ uncountable state space ⓘ
characterizedBy	initial distribution ⓘ state space ⓘ transition kernel ⓘ transition probabilities ⓘ
contrastsWith	non-Markovian process ⓘ
dependsOn	current state only ⓘ
doesNotDependOn	past history given present state ⓘ
field	probability theory ⓘ stochastic processes ⓘ
formalizedAs	family of random variables indexed by time ⓘ
generalizationOf	Markov processes self-linksurface differs ⓘ surface form: Markov chain
hasApplication	modeling diffusion of particles ⓘ modeling population dynamics ⓘ modeling queues ⓘ modeling random walks ⓘ modeling stock prices ⓘ
hasProperty	Markov processes self-linksurface differs ⓘ surface form: Markov property Markov semigroup (in time-homogeneous case) ⓘ memoryless ⓘ
hasSubtype	Markov chain ⓘ Markov decision process ⓘ Markov processes self-linksurface differs ⓘ surface form: Markov jump process birth–death process ⓘ continuous-time Markov process ⓘ diffusion process ⓘ discrete-time Markov process ⓘ hidden Markov model ⓘ
namedAfter	Andrey Markov ⓘ
relatedTo	Chapman–Kolmogorov equation ⓘ Kolmogorov backward equation ⓘ Fokker–Planck equation ⓘ surface form: Kolmogorov forward equation
timeIndex	continuous time ⓘ discrete time ⓘ
usedIn	biology ⓘ control theory ⓘ finance ⓘ information theory ⓘ Communication Nets: Stochastic Message Flow and Delay ⓘ surface form: queueing theory reinforcement learning ⓘ signal processing ⓘ statistical physics ⓘ

How these facts were elicited

The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.

Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
- If you don't know the subject at all, return an empty list.
- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: Markov processes
Description of subject: Markov processes are stochastic processes in which the future evolution depends only on the present state and not on the past history.

Referenced by (37)

Full triples — surface form annotated when it differs from this entity's canonical label.

Fokker–Planck equation → models → Markov processes ⓘ

Ornstein–Uhlenbeck process → hasProperty → Markov processes ⓘ

this entity surface form: Markov property

Ornstein–Uhlenbeck process → specialCaseOf → Markov processes ⓘ

this entity surface form: Gaussian Markov process

Markov processes → hasProperty → Markov processes self-linksurface differs ⓘ

subject surface form: Markov process

this entity surface form: Markov property

Markov processes → hasSubtype → Markov processes self-linksurface differs ⓘ

subject surface form: Markov process

this entity surface form: Markov jump process

Markov processes → generalizationOf → Markov processes self-linksurface differs ⓘ

subject surface form: Markov process

this entity surface form: Markov chain

Markov chain Monte Carlo → uses → Markov processes ⓘ

this entity surface form: Markov chain

Markov chain Monte Carlo → basedOn → Markov processes ⓘ

this entity surface form: Markov property

Kolmogorov backward equation → appliesTo → Markov processes ⓘ

PageRank algorithm → basedOn → Markov processes ⓘ

subject surface form: PageRank

this entity surface form: Markov chain

Random Walk and the Theory of Brownian Motion → usesConcept → Markov processes ⓘ

this entity surface form: Markov property

Iannis Xenakis → usedMathematicalConcept → Markov processes ⓘ

this entity surface form: Markov chains

Innovations approach to detection and estimation → usesConcept → Markov processes ⓘ

Probability Theory → usesConcept → Markov processes ⓘ

subject surface form: Probability theory

this entity surface form: Markov chain

Probability Theory → hasSubfield → Markov processes ⓘ

subject surface form: Probability theory

Viterbi algorithm → basedOn → Markov processes ⓘ

this entity surface form: Markov property

Andrey Markov → notableWork → Markov processes ⓘ

this entity surface form: Markov chains

Andrey Markov → notableWork → Markov processes ⓘ

Andrey Markov → notableIdea → Markov processes ⓘ

this entity surface form: Markov property

Chapman–Kolmogorov equation → field → Markov processes ⓘ

Chapman–Kolmogorov equation → appliesTo → Markov processes ⓘ

this entity surface form: Markov chains

Chapman–Kolmogorov equation → usedIn → Markov processes ⓘ

this entity surface form: Markov chain theory

Metropolis algorithm → uses → Markov processes ⓘ

this entity surface form: Markov chain

Gibbs sampling → basedOn → Markov processes ⓘ

this entity surface form: Markov chain theory

Markov random fields → satisfies → Markov processes ⓘ

subject surface form: Markov random field

this entity surface form: Markov property

Markov semigroup → usedIn → Markov processes ⓘ

this entity surface form: Markov process theory

Markov semigroup → usedIn → Markov processes ⓘ

this entity surface form: Markov chains

NIDA Division of Therapeutics and Medical Consequences → abbreviation → Markov processes ⓘ

this entity surface form: DTMC

detailed balance principle → field → Markov processes ⓘ

Modern Probability Theory and Its Applications → subject → Markov processes ⓘ

this entity surface form: Markov chains

Stochastic Processes → topic → Markov processes ⓘ

Introduction to Stochastic Control Theory → subject → Markov processes ⓘ

this entity surface form: Markov decision processes

Soviet school of probability theory → notableWork → Markov processes ⓘ

Kishor S. Trivedi → hasResearchInterest → Markov processes ⓘ

this entity surface form: Markov chains

Boltzmann–Kac equation → usesConcept → Markov processes ⓘ

this entity surface form: Markov process

Sheldon M. Ross (born Sheldon M. Frisch) → hasWrittenOn → Markov processes ⓘ

subject surface form: Sheldon M. Ross

this entity surface form: Markov chains