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2017 Long time asymptotics of unbounded additive functionals of Markov processes
Fuqing Gao
Electron. J. Probab. 22: 1-21 (2017). DOI: 10.1214/17-EJP104

Abstract

Under hypercontractivity and $L_p$-integrability of transition density for some $p>1$, we use the perturbation theory of linear operators to obtain existence of long time asymptotics of exponentials of unbounded additive functionals of Markov processes and establish the moderate deviation principle for the functionals. For stochastic differential equations with multiplicative noise, we show the hypercontractivity and the integrability based on Wang’s Harnack inequality. As an application of our general results, we obtain the existence of these asymptotics and the moderate deviation principle of additive functionals with quadratic growth for the stochastic differential equations with multiplicative noise under some explicit conditions on the coefficients and prove that these asymptotics solve the related ergodic Hamilton-Jacobi-Bellman equation with nonsmooth and quadratic growth cost in viscosity sense.

Citation

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Fuqing Gao. "Long time asymptotics of unbounded additive functionals of Markov processes." Electron. J. Probab. 22 1 - 21, 2017. https://doi.org/10.1214/17-EJP104

Information

Received: 29 March 2017; Accepted: 6 September 2017; Published: 2017
First available in Project Euclid: 1 November 2017

zbMATH: 06827071
MathSciNet: MR3724562
Digital Object Identifier: 10.1214/17-EJP104

Subjects:
Primary: 47A55 , 60F10 , 60H10 , 60J55

Keywords: additive functional , hypercontractivity , long time asymptotics , Moderate deviation , Perturbation theory

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