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.

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All labels observed (14)

Label	Occurrences
Markov processes canonical	15
Markov chains	14
Markov chain	8
Markov property	8
Markov chain theory	4
Markov jump process	2
Markov process	2
DTMC	1
Gaussian Markov process	1
Markov Processes from K. Itô’s Perspective	1
Markov assumption	1
Markov decision processes	1
Markov models	1
Markov process theory	1

How this entity was disambiguated

This entity first appeared as the object of triple T378952 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Markov processes
Context triple: [Fokker–Planck equation, models, Markov processes]

A. Markov chain Monte Carlo
Markov chain Monte Carlo is a class of algorithms that uses Markov chains to generate samples from complex probability distributions, widely used in Bayesian inference, statistical physics, and machine learning.
B. Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
C. Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
D. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
E. Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

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

A. Markov chain Monte Carlo
Markov chain Monte Carlo is a class of algorithms that uses Markov chains to generate samples from complex probability distributions, widely used in Bayesian inference, statistical physics, and machine learning.
B. Brownian motion
Brownian motion is the random, jittery movement of microscopic particles suspended in a fluid, whose explanation provided key evidence for the existence of atoms and the molecular nature of matter.
C. Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
D. Fokker–Planck equation
The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
E. Itô calculus
Itô calculus is a branch of stochastic analysis that extends classical calculus to functions of stochastic processes, particularly Brownian motion, enabling rigorous treatment of stochastic differential equations.
F. None of above. chosen

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 chain ⓘ linked to: Markov processes
hasApplication	modeling diffusion of particles ⓘ modeling population dynamics ⓘ modeling queues ⓘ modeling random walks ⓘ modeling stock prices ⓘ
hasProperty	Markov property ⓘ linked to: Markov processes Markov semigroup (in time-homogeneous case) ⓘ memoryless ⓘ
hasSubtype	Markov chain ⓘ Markov decision process ⓘ Markov jump process ⓘ linked to: Markov processes 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 ⓘ Kolmogorov forward equation ⓘ linked to: Fokker–Planck equation
timeIndex	continuous time ⓘ discrete time ⓘ
usedIn	biology ⓘ control theory ⓘ finance ⓘ information theory ⓘ queueing theory ⓘ linked to: Communication Nets: Stochastic Message Flow and Delay reinforcement learning ⓘ signal processing ⓘ statistical physics ⓘ

How these facts were elicited

Referenced by (60)

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 property ⓘ

linked to: Markov processes

Ornstein–Uhlenbeck process → specialCaseOf → Gaussian Markov process ⓘ

linked to: Markov processes

Markov process → hasProperty → Markov property ⓘ

subject linked to: Markov processes

linked to: Markov processes

Markov process → hasSubtype → Markov jump process ⓘ

subject linked to: Markov processes

linked to: Markov processes

Markov process → generalizationOf → Markov chain ⓘ

subject linked to: Markov processes

linked to: Markov processes

Markov chain Monte Carlo → uses → Markov chain ⓘ

linked to: Markov processes

Markov chain Monte Carlo → basedOn → Markov property ⓘ

linked to: Markov processes

Kolmogorov backward equation → appliesTo → Markov processes ⓘ

PageRank → basedOn → Markov chain ⓘ

subject linked to: PageRank algorithm

linked to: Markov processes

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

linked to: Markov processes

Iannis Xenakis → usedMathematicalConcept → Markov chains ⓘ

linked to: Markov processes

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

Probability theory → usesConcept → Markov chain ⓘ

subject linked to: Probability Theory

linked to: Markov processes

Probability theory → hasSubfield → Markov processes ⓘ

subject linked to: Probability Theory

Viterbi algorithm → basedOn → Markov property ⓘ

linked to: Markov processes

Andrey Markov → notableWork → Markov chains ⓘ

linked to: Markov processes

Andrey Markov → notableWork → Markov processes ⓘ

Andrey Markov → notableIdea → Markov property ⓘ

linked to: Markov processes

Chapman–Kolmogorov equation → field → Markov processes ⓘ

Chapman–Kolmogorov equation → appliesTo → Markov processes ⓘ

Chapman–Kolmogorov equation → appliesTo → Markov chains ⓘ

linked to: Markov processes

Chapman–Kolmogorov equation → usedIn → Markov chain theory ⓘ

linked to: Markov processes

Metropolis algorithm → uses → Markov chain ⓘ

linked to: Markov processes

Gibbs sampling → basedOn → Markov chain theory ⓘ

linked to: Markov processes

Markov random field → satisfies → Markov property ⓘ

subject linked to: Markov random fields

linked to: Markov processes

Markov semigroup → usedIn → Markov process theory ⓘ

linked to: Markov processes

Markov semigroup → usedIn → Markov chains ⓘ

linked to: Markov processes

NIDA Division of Therapeutics and Medical Consequences → abbreviation → DTMC ⓘ

linked to: Markov processes

detailed balance principle → field → Markov processes ⓘ

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

linked to: Markov processes

Stochastic Processes → topic → Markov processes ⓘ

Introduction to Stochastic Control Theory → subject → Markov decision processes ⓘ

linked to: Markov processes

Soviet school of probability theory → notableWork → Markov processes ⓘ

Kishor S. Trivedi → hasResearchInterest → Markov chains ⓘ

linked to: Markov processes

Boltzmann–Kac equation → usesConcept → Markov process ⓘ

linked to: Markov processes

Sheldon M. Ross → hasWrittenOn → Markov chains ⓘ

subject linked to: Sheldon M. Ross (born Sheldon M. Frisch)

linked to: Markov processes

Markov localization → basedOn → Markov assumption ⓘ

linked to: Markov processes

Daniel Stroock → notableWork → Markov Processes from K. Itô’s Perspective ⓘ

linked to: Markov processes

Poisson process → hasProperty → Markov property ⓘ

linked to: Markov processes

Poisson process → isSpecialCaseOf → Markov jump process ⓘ

linked to: Markov processes

graph Laplacian → usedIn → Markov chains ⓘ

linked to: Markov processes

Spectral Graph Theory → relatedTo → Markov chains ⓘ

linked to: Markov processes

Pólya’s theorem on random walks → usedIn → Markov chain theory ⓘ

linked to: Markov processes

Elements of Information Theory → subject → Markov chains ⓘ

linked to: Markov processes

Freidlin–Wentzell theory → appliesTo → Markov processes ⓘ

Systems in Stochastic Equilibrium → mainSubject → Markov processes ⓘ

Optimization over Time → topic → Markov chains ⓘ

linked to: Markov processes

Ehrenfest model → mathematicalTool → Markov chain theory ⓘ

linked to: Markov processes

Peter Doyle (mathematician) → hasResearchArea → Markov chains ⓘ

linked to: Markov processes

All labels observed (14)

How this entity was disambiguated Show

Statements (50)

How these facts were elicited Show

Referenced by (60)

How this entity was disambiguated

How these facts were elicited