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.

ON A SUFFICIENT CONDITION FOR LARGE DEVIATIONS OF ADDITIVE FUNCTIONALS

2011 ◽  
Vol 11 (01) ◽  
pp. 157-181 ◽  
Author(s):  
KANEHARU TSUCHIDA
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Markov Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Processes ◽  
Sufficient Condition ◽  
Additive Functionals ◽  
Deviation Principle ◽  
Symmetric Markov Processes

We prove the large deviation principle for continuous additive functionals under certain assumptions. The underlying symmetric Markov processes include Brownian motion and symmetric and relativistic α-stable processes.

A LARGE DEVIATION FOR OCCUPATION TIME OF SUPER α-STABLE PROCESS

2008 ◽  
Vol 11 (01) ◽  
pp. 53-71 ◽  
Author(s):  
QIU-YUE LI ◽  
YAN-XIA REN
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Stable Process ◽  
Rate Function ◽  
Occupation Time ◽  
Occupation Times ◽  
Tail Probabilities ◽  
Super Brownian Motion

We derive a large deviation principle for occupation time of super α-stable process in ℝd with d > 2α. The decay of tail probabilities is shown to be exponential and the rate function is characterized. Our result can be considered as a counterpart of Lee's work on large deviations for occupation times of super-Brownian motion in ℝd for dimension d > 4 (see Ref. 10).

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

2006 ◽  
Vol 06 (04) ◽  
pp. 487-520 ◽  
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.

scholarly journals Large deviations for stochastic integrodifferential equations of the Itô type with multiple randomness

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 473-487 ◽  
Author(s):  
A. Haseena ◽  
M. Suvinthra ◽  
N. Annapoorani
Keyword(s):  
Weak Convergence ◽  
Large Deviations ◽  
Finite Number ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Integrodifferential Equations ◽  
Multiplicative Noises ◽  
Deviation Principle ◽  
Laplace Principle ◽  
Weak Convergence Approach

A Freidlin-Wentzell type large deviation principle is derived for a class of It? type stochastic integrodifferential equations driven by a finite number of multiplicative noises of the Gaussian type. The weak convergence approach is used here to prove the Laplace principle, equivalently large deviation principle.

Large deviations for super-Brownian motion with immigration

2004 ◽  
Vol 41 (01) ◽  
pp. 187-201 ◽  
Author(s):  
Mei Zhang
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Lebesgue Measure ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Time Process ◽  
Super Brownian Motion ◽  
Speed Function ◽  
Occupation Time Process ◽  
Random Immigration

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function ist1/2ford= 1,t/logtford= 2 andtford≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.

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].

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