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In the paper, we consider nonlinear filtering problems of multiscale systems in two cases-correlated sensor Levy noises and correlated Levy noises. First of all, we prove that the slow part of the origin system converges to the homogenized system in the uniform mean square sense. And then based on the convergence result, in the case of correlated sensor Levy noises, the nonlinear filtering of the slow part is shown to approximate that of the homogenized system in $L^1$ sense. However, in the case of correlated Levy noises, we prove that the nonlinear filtering of the slow part converges weakly to that of the homogenized system.
The objective in stochastic filtering is to reconstruct information about an unobserved (random) process, called the signal process, given the current available observations of a certain noisy transformation of that process. Usually X and Y are mod
In this paper, we study the Besov regularity of Levy white noises on the $d$-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results
Stochastic models of chemical reaction networks are an important tool to describe and analyze noise effects in cell biology. When chemical species and reaction rates in a reaction system have different orders of magnitude, the associated stochastic s
We consider stochastic difference equation x_{n+1} = x_n (1 - h f(x_n) + sqrt{h} g(x_n) xi_{n+1}), where functions f and g are nonlinear and bounded, random variables xi_i are independent and h>0 is a nonrandom parameter. We establish results on asym
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates f