Large deviation principle for additive functionals of semi-Markov processes

2021 ◽  
pp. 1-19
Author(s):  
Adina Oprisan
Keyword(s):  
Markov Processes ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Additive Functionals ◽  
Deviation Principle ◽  
Semi Markov Processes

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.

scholarly journals Local large deviation principle for Wiener process with random resetting

2019 ◽  
Vol 20 (05) ◽  
pp. 2050032
Author(s):  
A. Logachov ◽  
O. Logachova ◽  
A. Yambartsev
Keyword(s):  
Population Dynamics ◽  
Markov Processes ◽  
Conditional Distribution ◽  
Arrival Time ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Deviation Principle ◽  
Wiener Processes ◽  
Random Times ◽  
Local Large Deviation Principle

We consider a class of Markov processes with resettings, where at random times, the Markov processes are restarted from a predetermined point or a region. These processes are frequently applied in physics, chemistry, biology, economics, and in population dynamics. In this paper, we establish the local large deviation principle (LLDP) for the Wiener processes with random resettings, where the resettings occur at the arrival time of a Poisson process. Here, at each resetting time, a new resetting point is selected at random, according to a conditional distribution.

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.

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.

Large deviation principle for the field in prequantum classical statistical field theory

2017 ◽  
Vol 20 (04) ◽  
pp. 1750025
Author(s):  
Andrei Khrennikov ◽  
Achref Majid
Keyword(s):  
Field Theory ◽  
Random Field ◽  
Field Model ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Background Field ◽  
Deviation Principle ◽  
Statistical Field ◽  
Statistical Field Theory

In this paper, we prove a large deviation principle for the background field in prequantum statistical field model. We show a number of examples by choosing a specific random field in our model.

Sign in / Sign up

Export Citation Format

Share Document