Markov processes
E48274
Markov processes are stochastic processes in which the future evolution depends only on the present state and not on the past history.
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 |
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 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.
this entity surface form:
Markov property
this entity surface form:
Gaussian Markov process
subject surface form:
Markov process
this entity surface form:
Markov property
subject surface form:
Markov process
this entity surface form:
Markov jump process
subject surface form:
Markov process
this entity surface form:
Markov chain
this entity surface form:
Markov chain
this entity surface form:
Markov property
subject surface form:
PageRank
this entity surface form:
Markov chain
this entity surface form:
Markov property
this entity surface form:
Markov chains
subject surface form:
Probability theory
this entity surface form:
Markov chain
subject surface form:
Probability theory
this entity surface form:
Markov property
this entity surface form:
Markov chains
this entity surface form:
Markov property
this entity surface form:
Markov chains
this entity surface form:
Markov chain theory
this entity surface form:
Markov chain
this entity surface form:
Markov chain theory
subject surface form:
Markov random field
this entity surface form:
Markov property
this entity surface form:
Markov process theory
this entity surface form:
Markov chains
this entity surface form:
DTMC
this entity surface form:
Markov chains
this entity surface form:
Markov decision processes
this entity surface form:
Markov chains
this entity surface form:
Markov process
subject surface form:
Sheldon M. Ross
this entity surface form:
Markov chains