Geodesic
Large deviation principle for processes with Poisson noise term
Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 59-76

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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.
Keywords: Large deviations, rate functional, Poisson measure, telegraph signal process. 
A. V. Logachov. Large deviation principle for processes with Poisson noise term. Teoriâ slučajnyh processov, Tome 18 (2012) no. 2, pp. 59-76. http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a6/
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