scholarly journals Large deviations for Markov processes with stochastic resetting: analysis via the empirical density and flows or via excursions between resets

2021 ◽  
Vol 2021 (3) ◽  
pp. 033201
Author(s):  
Cécile Monthus
Keyword(s):  
Large Deviations ◽  
Markov Processes ◽  
Empirical Density

scholarly journals Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment

2022 ◽  
Vol 2022 (1) ◽  
pp. 013206
Author(s):  
Cécile Monthus
Keyword(s):  
Large Deviations ◽  
Markov Processes ◽  
Large Time ◽  
Diffusion Processes ◽  
Large Deviation ◽  
Time Window ◽  
Extinction Rate ◽  
Empirical Density ◽  
Full Optimization ◽  
Absorbing States

Abstract The large deviations at level 2.5 are applied to Markov processes with absorbing states in order to obtain the explicit extinction rate of metastable quasi-stationary states in terms of their empirical time-averaged density and of their time-averaged empirical flows over a large time-window T. The standard spectral problem for the slowest relaxation mode can be recovered from the full optimization of the extinction rate over all these empirical observables and the equivalence can be understood via the Doob generator of the process conditioned to survive up to time T. The large deviation properties of any time-additive observable of the Markov trajectory before extinction can be derived from the level 2.5 via the decomposition of the time-additive observable in terms of the empirical density and the empirical flows. This general formalism is described for continuous-time Markov chains, with applications to population birth–death model in a stable or in a switching environment, and for diffusion processes in dimension d.

scholarly journals A Note on Rényi's ‘Record’ Problem and Engel's Series

2018 ◽  
Vol 61 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Lulu Fang ◽  
Min Wu
Keyword(s):  
Number Theory ◽  
Large Deviations ◽  
Markov Processes ◽  
Classical Limit ◽  
Limit Theorems ◽  
London Math ◽  
Law Of Large Numbers ◽  
Record Times ◽  
Iterated Logarithm ◽  
Large Numbers

AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] introduced two interesting discrete Markov processes, namely C-processes and A-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there is a difference between C-processes and A-processes in the context of large deviations.

scholarly journals Adaptive control of discrete time Markov processes by the large deviations method

2000 ◽  
Vol 27 (3) ◽  
pp. 265-285 ◽  
Author(s):  
T. Duncan ◽  
B. Pasik-Duncan ◽  
Łukasz Stettner
Keyword(s):  
Adaptive Control ◽  
Large Deviations ◽  
Markov Processes ◽  
Discrete Time

scholarly journals Laplace Approximations for Large Deviations of Nonreversible Markov Processes. The Nondegenerate Case

1995 ◽  
Vol 23 (1) ◽  
pp. 236-267 ◽  
Author(s):  
Erwin Bolthausen ◽  
Jean-Dominique Deuschel ◽  
Yozo Tamura
Keyword(s):  
Large Deviations ◽  
Markov Processes ◽  
Nondegenerate Case

Some Notes on Large Deviations of Markov Processes

2000 ◽  
Vol 16 (3) ◽  
pp. 369-394 ◽  
Author(s):  
Liming Wu
Keyword(s):  
Large Deviations ◽  
Markov Processes
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