Large Deviations for Stochastic Differential Equations on Sd Associated with the Critical Sobolev Brownian Vector Fields

International Journal of Stochastic Analysis ◽

10.1155/2011/840908 ◽

2011 ◽

Vol 2011 ◽

pp. 1-19

Author(s):

Qinghua Wang

Keyword(s):

Differential Equations ◽

Large Deviations ◽

Stochastic Differential Equations ◽

Vector Fields ◽

Large Deviation Principle ◽

Large Deviation ◽

Deviation Principle

We obtain a large deviation principle for the stochastic differential equations on the sphere Sd associated with the critical Sobolev Brownian vector fields.

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Large deviations for stochastic differential equations with general delayed generator

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2039 ◽

2020 ◽

Vol 28 (3) ◽

pp. 197-207

Author(s):

Clément Manga ◽

Auguste Aman

Keyword(s):

Differential Equations ◽

Large Deviations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Differential Delay ◽

Deviation Principle ◽

Nonlinear Anal ◽

Differential Delay Equations ◽

Stochastic Differential Delay Equations

AbstractThis paper is devoted to derive a Freidlin–Wentzell type of the large deviation principle for stochastic differential equations with general delayed generator. We improve the result of Chi Mo and Jiaowan Luo [C. Mo and J. Luo, Large deviations for stochastic differential delay equations, Nonlinear Anal. 80 2013, 202–210].

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LARGE DEVIATION PRINCIPLES FOR ISOTROPIC STOCHASTIC FLOW OF HOMEOMORPHISMS ON Sd

Stochastics and Dynamics ◽

10.1142/s0219493710003042 ◽

2010 ◽

Vol 10 (04) ◽

pp. 465-495 ◽

Cited By ~ 1

Author(s):

TIANGE XU ◽

TUSHENG ZHANG

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Vector Fields ◽

Large Deviation Principle ◽

Large Deviation ◽

Stochastic Flow ◽

Deviation Principle ◽

Large Deviation Principles

In this paper, we obtain a large deviation principle for the flow of homeomorphisms of the stochastic differential equations on the sphere Sd associated with the critical Sobolev Brownian vector fields.

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Small double limit with reflecting Wentzel boundary condition

Random Operators and Stochastic Equations ◽

10.1515/rose-2021-2066 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Ibrahima Sane ◽

Alassane Diedhiou

Keyword(s):

Boundary Condition ◽

Differential Equations ◽

Large Deviations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Rate Function ◽

Deviation Principle ◽

Two Parameters ◽

Double Limit

Abstract We provide a large deviation principle on the stochastic differential equations with reflecting Wentzel boundary condition if δ ε {\frac{\delta}{\varepsilon}} tends to 0 when the two parameters δ (homogenization parameter) and ε (the large deviations parameter) tend to zero. Here, we suppose that the homogenization parameter converges sufficiently quickly more than the large deviations parameter. Furthermore, we will make explicit the associated rate function.

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Diffusion processes on graphs: stochastic differential equations, large deviation principle

Probability Theory and Related Fields ◽

10.1007/pl00008726 ◽

2000 ◽

Vol 116 (2) ◽

pp. 181-220 ◽

Cited By ~ 35

Author(s):

Mark Freidlin ◽

Shuenn-Jyi Sheu

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Diffusion Processes ◽

Large Deviation ◽

Deviation Principle

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Asymptotic properties of coupled forward–backward stochastic differential equations

Stochastics and Dynamics ◽

10.1142/s021949371450004x ◽

2014 ◽

Vol 14 (03) ◽

pp. 1450004 ◽

Cited By ~ 1

Author(s):

Ana Bela Cruzeiro ◽

André de Oliveira Gomes ◽

Liangquan Zhang

Keyword(s):

Asymptotic Behavior ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Asymptotic Properties ◽

Backward Stochastic Differential Equations ◽

Type Formula ◽

Deviation Principle

In this paper, we consider coupled forward–backward stochastic differential equations (FBSDEs in short) with parameter ε > 0, of the following type [Formula: see text] We study the asymptotic behavior of its solutions and establish a large deviation principle for the corresponding processes.

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Large deviation principle for reflected Poisson driven stochastic differential equations in epidemic models

Stochastic Analysis and Applications ◽

10.1080/07362994.2019.1616556 ◽

2019 ◽

Vol 37 (5) ◽

pp. 836-864 ◽

Cited By ~ 1

Author(s):

Etienne Pardoux ◽

Brice Samegni-Kepgnou

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Epidemic Models ◽

Deviation Principle

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Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales

Stochastic Processes and their Applications ◽

10.1016/j.spa.2017.09.011 ◽

2018 ◽

Vol 128 (7) ◽

pp. 2179-2227

Author(s):

Arnab Ganguly

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Stochastic Integrals ◽

Infinite Dimensional ◽

Deviation Principle

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Large deviation principle of stochastic differential equations with non-Lipschitzian coefficients

Frontiers of Mathematics in China ◽

10.1007/s11464-013-0318-6 ◽

2013 ◽

Vol 8 (6) ◽

pp. 1307-1321 ◽

Cited By ~ 1

Author(s):

Guangqiang Lan

Keyword(s):

Differential Equations ◽

Stochastic Differential Equations ◽

Large Deviation Principle ◽

Large Deviation ◽

Deviation Principle

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LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

Stochastics and Dynamics ◽

10.1142/s0219493710002978 ◽

2010 ◽

Vol 10 (03) ◽

pp. 315-339 ◽

Cited By ~ 2

Author(s):

A. A. DOROGOVTSEV ◽

O. V. OSTAPENKO

Keyword(s):

Brownian Motion ◽

Large Deviations ◽

Large Deviation Principle ◽

Large Deviation ◽

Stochastic Flows ◽

Brownian Motions ◽

Deviation Principle ◽

And Brownian Motion

We establish the large deviation principle (LDP) for stochastic flows of interacting Brownian motions. In particular, we consider smoothly correlated flows, coalescing flows and Brownian motion stopped at a hitting moment.

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LARGE DEVIATIONS FOR SMALL PERTURBATIONS OF SDES WITH NON-MARKOVIAN COEFFICIENTS AND THEIR APPLICATIONS

Stochastics and Dynamics ◽

10.1142/s0219493706001840 ◽

2006 ◽

Vol 06 (04) ◽

pp. 487-520 ◽

Cited By ~ 1

Author(s):

FUQING GAO ◽

JICHENG LIU

Keyword(s):

Large Deviations ◽

Large Deviation Principle ◽

Large Deviation ◽

Wiener Space ◽

Small Perturbations ◽

Deviation Principle ◽

Large Deviation Principles ◽

Sobolev Norms

We prove large deviation principles for solutions of small perturbations of SDEs in Hölder norms and Sobolev norms, where the SDEs have non-Markovian coefficients. As an application, we obtain a large deviation principle for solutions of anticipating SDEs in terms of (r, p) capacities on the Wiener space.

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