Small double limit with reflecting Wentzel boundary condition

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.

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

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.

Large deviations for stochastic differential equations with general delayed generator

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].

scholarly journals Asymptotic properties of coupled forward–backward stochastic differential equations

2014 ◽  
Vol 14 (03) ◽  
pp. 1450004 ◽  
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.

LARGE DEVIATION PRINCIPLES FOR ISOTROPIC STOCHASTIC FLOW OF HOMEOMORPHISMS ON Sd

2010 ◽  
Vol 10 (04) ◽  
pp. 465-495 ◽  
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.

scholarly journals LARGE DEVIATIONS FOR FLOWS OF INTERACTING BROWNIAN MOTIONS

2010 ◽  
Vol 10 (03) ◽  
pp. 315-339 ◽  
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.

scholarly journals The Large Deviations of Estimating Rate Functions

2005 ◽  
Vol 42 (01) ◽  
pp. 267-274 ◽  
Author(s):  
Ken Duffy ◽  
Anthony P. Metcalfe
Keyword(s):  
Large Deviation Principle ◽  
Large Deviation ◽  
Length Distribution ◽  
Rate Function ◽  
Partial Sums ◽  
Single Server ◽  
Mixing Condition ◽  
Deviation Principle ◽  
Queue Length Distribution ◽  
Empirical Estimates

Given a sequence of bounded random variables that satisfies a well-known mixing condition, it is shown that empirical estimates of the rate function for the partial sums process satisfy the large deviation principle in the space of convex functions equipped with the Attouch-Wets topology. As an application, a large deviation principle for estimating the exponent in the tail of the queue length distribution at a single-server queue with infinite waiting space is proved.

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