Freidlin–Wentzell theory

E653522

large deviations theory mathematical theory probability theory

Freidlin–Wentzell theory is a mathematical framework in probability that analyzes the behavior of stochastic dynamical systems under small random perturbations using large deviation principles.

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Statements (45)

Predicate	Object
instanceOf	large deviations theory ⓘ mathematical theory ⓘ probability theory ⓘ
appliesTo	Markov processes NERFINISHED ⓘ ordinary differential equations with noise ⓘ stochastic differential equations ⓘ
assumes	small noise limit ⓘ
basedOn	large deviations for trajectories of stochastic processes ⓘ
characterizes	exponential decay of probabilities of rare events ⓘ most probable paths of rare transitions ⓘ
describedIn	Random Perturbations of Dynamical Systems NERFINISHED ⓘ
developedIn	20th century ⓘ
field	dynamical systems ⓘ probability theory ⓘ stochastic processes ⓘ
focusesOn	asymptotic behavior of stochastic systems ⓘ small random perturbations ⓘ stochastic dynamical systems ⓘ
hasApplicationIn	chemical reaction networks ⓘ climate dynamics ⓘ engineering reliability ⓘ population dynamics ⓘ statistical physics ⓘ
hasKeyResult	asymptotics of exit time distributions ⓘ asymptotics of invariant measures under small noise ⓘ large deviation principle for trajectories of diffusions ⓘ
mainReferenceAuthor	Alexander Wentzell NERFINISHED ⓘ Mark Freidlin NERFINISHED ⓘ
namedAfter	Alexander Wentzell NERFINISHED ⓘ Mark Freidlin NERFINISHED ⓘ
provides	exponential estimates for exit times ⓘ framework for metastable behavior analysis ⓘ variational characterization of transition paths ⓘ
relatedTo	Donsker–Varadhan theory NERFINISHED ⓘ WKB approximation NERFINISHED ⓘ stochastic stability theory ⓘ
studies	exit problems from domains ⓘ metastability ⓘ quasi-potential ⓘ rare events ⓘ transition probabilities between attractors ⓘ
usesConcept	action functional ⓘ exponential estimates of probabilities ⓘ large deviation principle ⓘ rate function ⓘ

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