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.

Differentiability of spectral functions for nearly stable processes and large deviations

2014 ◽  
Vol 17 (03) ◽  
pp. 1450017
Author(s):  
Yoshihiro Tawara ◽  
Kaneharu Tsuchida
Keyword(s):  
Large Deviations ◽  
Spectral Function ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Characteristic Exponent ◽  
Stable Processes ◽  
Slowly Varying Function ◽  
Spectral Functions ◽  
Additive Functionals ◽  
Deviation Principle

We consider the differentiability of a spectral function generated by a Lévy process M with characteristic exponent |ξ|αl(|ξ|2), where l(x) is a slowly varying function at ∞. As an application, we obtain the large deviation principle for positive continuous additive functionals of M. Finally, we show that the exponent l(x) = ( log (1 + x))β/2 (0 < β < 2 - α) is an example for which our theorem is applicable.

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 Large deviations for unbounded additive functionals of a Markov process with discrete time (noncompact case)

1994 ◽  
Vol 7 (3) ◽  
pp. 423-436 ◽  
Author(s):  
O. V. Gulinskii ◽  
Robert S. Lipster ◽  
S. V. Lototskii
Keyword(s):  
Markov Process ◽  
Large Deviations ◽  
Discrete Time ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Occupation Measure ◽  
Additive Functionals ◽  
Deviation Principle ◽  
Exponential Tightness

We combine the Donsker and Varadhan large deviation principle (l.d.p) for the occupation measure of a Markov process with certain results of Deuschel and Stroock, to obtain the l.d.p. for unbounded functionals. Our approach relies on the concept of exponential tightness and on the Puhalskii theorem. Three illustrative examples are considered.

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.

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