Dynkin formula
E262081
Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Dynkin formula canonical | 1 |
| Dynkin formula for killed processes | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2393112 — 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: Dynkin formula Context triple: [Kolmogorov backward equation, relatedTo, Dynkin formula]
-
A.
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.
-
B.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
-
C.
Doob–Meyer decomposition
The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
- 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: Dynkin formula Target entity description: Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
-
A.
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.
-
B.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
-
C.
Doob–Meyer decomposition
The Doob–Meyer decomposition is a fundamental result in stochastic process theory that uniquely expresses a submartingale as the sum of a martingale and a predictable, increasing process.
-
D.
Kolmogorov backward equation
The Kolmogorov backward equation is a fundamental partial differential equation in stochastic processes that characterizes the time evolution of expected values of functionals of Markov processes, complementary to the Fokker–Planck (forward) equation.
-
E.
Itô’s lemma
Itô’s lemma is a fundamental result in stochastic calculus that generalizes the chain rule to functions of stochastic processes, especially Brownian motion.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
result in Markov process theory
ⓘ
theorem in probability theory ⓘ |
| appliesTo |
Markov process
ⓘ
stopping time ⓘ time-homogeneous Markov process ⓘ |
| assumes |
Markov property
ⓘ
integrability conditions for the stopping time ⓘ sufficient regularity of the test function ⓘ |
| component |
Markov process (X_t)
ⓘ
generator L of the Markov process ⓘ stopping time τ ⓘ test function f on the state space ⓘ |
| expresses |
expectation as initial value plus time integral of the generator applied to the function
ⓘ
expected value of a function of the process at a stopping time ⓘ |
| field |
Markov processes
ⓘ
probability theory ⓘ stochastic processes ⓘ |
| generalizationOf |
Kolmogorov backward equation
ⓘ
surface form:
Kolmogorov backward equation for expectations
|
| hasForm | E[f(X_τ)] = f(X_0) + E[∫_0^τ Lf(X_s) ds] under suitable conditions ⓘ |
| hasVersion |
Dynkin formula
self-linksurface differs
ⓘ
surface form:
Dynkin formula for killed processes
local Dynkin formula ⓘ |
| holdsFor |
continuous-time Markov chains
ⓘ
diffusion processes ⓘ jump Markov processes ⓘ |
| implies | that f(X_t) − f(X_0) − ∫_0^t Lf(X_s) ds is a martingale ⓘ |
| mathematicalNature | identity for expectations of Markov processes ⓘ |
| namedAfter | Eugene Dynkin ⓘ |
| relatedTo |
Feynman–Kac formula
ⓘ
martingale problem of Stroock–Varadhan ⓘ |
| relatesConcept |
Itô’s lemma
ⓘ
surface form:
Itô formula
Kolmogorov backward equation ⓘ expected value of functionals of a process ⓘ infinitesimal generator of a Markov process ⓘ martingale methods ⓘ |
| stateSpace | general measurable state space ⓘ |
| timeDomain | continuous time ⓘ |
| typicalCondition |
bounded stopping time or suitable integrability
ⓘ
f in the domain of the generator L ⓘ |
| usedFor |
characterizing harmonic functions for Markov processes
ⓘ
deriving partial differential equations for expectations ⓘ proving uniqueness of solutions to martingale problems ⓘ solving boundary value problems in probability ⓘ verification of solutions to stochastic control problems ⓘ |
| usedIn |
applied probability
ⓘ
mathematical finance ⓘ potential theory of Markov processes ⓘ queueing theory ⓘ stochastic control theory ⓘ |
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
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Input
Subject: Dynkin formula Description of subject: Dynkin formula is a fundamental result in the theory of Markov processes that expresses the expected value of a function of the process at a stopping time in terms of its generator and an integral over time.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dynkin formula for killed processes