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.
Aliases (6)
- Markov process ×50
- Markov property ×4
- Markov chain ×3
- Gaussian Markov process ×1
- Markov chains ×1
- Markov jump process ×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 chain
→
|
| hasApplication |
modeling diffusion of particles
→
modeling population dynamics → modeling queues → modeling random walks → modeling stock prices → |
| hasProperty |
Markov property
→
Markov semigroup (in time-homogeneous case) → memoryless → |
| hasSubtype |
Markov chain
→
Markov decision process → 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 → Kolmogorov forward equation → |
| timeIndex |
continuous time
→
discrete time → |
| usedIn |
biology
→
control theory → finance → information theory → queueing theory → reinforcement learning → signal processing → statistical physics → |
Referenced by (12)
| Subject (surface form when different) | Predicate |
|---|---|
|
Markov chain Monte Carlo
("Markov property")
→
PageRank ("Markov chain") → |
basedOn |
|
Markov process
("Markov property")
→
Ornstein–Uhlenbeck process ("Markov property") → |
hasProperty |
|
Kolmogorov backward equation
→
|
appliesTo |
|
Markov process
("Markov chain")
→
|
generalizationOf |
|
Markov process
("Markov jump process")
→
|
hasSubtype |
|
Fokker–Planck equation
→
|
models |
|
Ornstein–Uhlenbeck process
("Gaussian Markov process")
→
|
specialCaseOf |
|
Iannis Xenakis
("Markov chains")
→
|
usedMathematicalConcept |
|
Markov chain Monte Carlo
("Markov chain")
→
|
uses |
|
Random Walk and the Theory of Brownian Motion
("Markov property")
→
|
usesConcept |