Large deviation principle for processes with Poisson noise term

A. Logachov
Theory of Stochastic Processes
Vol.18 (34), no.2, 2012, pp.59-76
Let $\tilde{\nu}_n(du,dt)$ be a centered Poisson measure with the parameter $n\Pi(du)dt,$ and let $a_n(t,\omega)$ and $f_n(u,t,\omega)$ be stochastic processes. The large deviation principle for the sequence $\eta_n(t)=x_0+\int\limits_0^t a_n(s)ds+\frac{1}{\sqrt{ n}\varphi(n)}\int\limits_0^t\int f_n(u,s)\tilde{\nu}_n(du,ds)$ is proved. As examples, the large deviation principles for the normalized integral of a telegraph signal and for stochastic differential equations with periodic coefficients are obtained.