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. 
@article{THSP_2012_18_2_a6,
     author = {A. V. Logachov},
     title = {Large deviation principle for processes with {Poisson} noise term},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {59--76},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2012_18_2_a6/}
}
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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/