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Itô diffusion

In mathematics – specifically, in stochastic analysis – an Itô diffusion is a solution to a specific type of stochastic differential equation. That equation is similar to the Langevin equation used in physics to describe the Brownian motion of a particle subjected to a potential in a viscous fluid. Itô diffusions are named after the Japanese…

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Overview

Continuity

The Markov property

The generator

Definition

The characteristic operator

The resolvent operator

Invariant measures

The martingale property

Dynkin's formula

Associated measures

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Itô diffusion

Nodes98
Edges97
Triples83
Avg. degree1.98
Density0.020408
Components1

How this topic connects Entity context

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Itô diffusion

Top relations

related to Definition · 10
Itô diffusion → Associated, C2, DA, Dirichlet, Formally, It, Itô, One, Rn, The
related to Dynkin's formula · 9
Itô diffusion → Brownian, C2, Dynkin's, Eugene Dynkin, Ex, For, Itô, Precisely, Rn
related to Invariant measures · 9
Itô diffusion → Conversely, Itô, Planck, Rn, Sometimes, The Fokker, This, X0, Xt
related to Feller continuity · 8
Itô diffusion → Ex, Feller-continuous, For, In, Itô, Px, Rn, X0
related to The harmonic measure · 8
Itô diffusion → Brownian, Bτ, For, In, Itô, Rn, Sometimes, That
related to The Green measure and Green formula · 7
Itô diffusion → Borel, Green, Intuitively, Itô, Let, Rn, That
related to The martingale property · 7
Itô diffusion → C2, However, In, Itô, Itô's, Rn, The
related to The resolvent operator · 7
Itô diffusion → For, However, In, Itô, Rn, Rα, The
related to The Markov property · 6
Itô diffusion → An Itô, Brownian, Let, Markovian, The, Xt
related to overview · 5
Itô diffusion → Brownian, Euclidean, Itô, Lipschitz, Rn

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Important terminology

rn diffusion itô process equation time operator differential measure generator function brownian motion defined invariant given bounded stochastic continuous xt

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Itô diffusionis asolution to a specific type of stochastic differential equation0.90text
Itô diffusionis acontinuous0.90text
Itô diffusionrelated to DefinitionAssociated0.60section
Itô diffusionrelated to DefinitionItô0.60section
Itô diffusionrelated to DefinitionThe0.60section
Itô diffusionrelated to DefinitionFormally0.60section
Itô diffusionrelated to DefinitionRn0.60section
Itô diffusionrelated to DefinitionDA0.60section
Itô diffusionrelated to DefinitionOne0.60section
Itô diffusionrelated to DefinitionC20.60section
Itô diffusionrelated to DefinitionIt0.60section
Itô diffusionrelated to DefinitionDirichlet0.60section

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