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Register a new userA Kolmogorov type theorem for stochastic fields
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We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solutions for nonlocal stochastic parabolic equations driven by non-Gaussian L{e}vy noises.
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We study the weak limits of solutions to SDEs [dX_n(t)=a_nbigl(X_n(t)bigr),dt+dW(t),] where the sequence ${a_n}$ converges in some sense to $(c_- 1mkern-4.5mumathrm{l}_{x<0}+c_+ 1mkern-4.5mumathrm{l}_{x>0})/x+gammadelta_0$. Here $delta_0$ is the Dirac delta function concentrated at zero. A limit of ${X_n}$ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.
We consider a particle undergoing Brownian motion in Euclidean space of any dimension, forced by a Gaussian random velocity field that is white in time and smooth in space. We show that conditional on the velocity field, the quenched density of the particle after a long time can be approximated pointwise by the product of a deterministic Gaussian density and a spacetime-stationary random field $U$. If the velocity field is additionally assumed to be incompressible, then $Uequiv 1$ almost surely and we obtain a local central limit theorem.
Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such conditions work but those already existing fail, are given as well. Key words and phrases: Anscombe theorem, Exchangeability, Random indices, Random sums, Stable convergence
In this paper we study the moderate deviations for the magnetization of critical Curie-Weiss model. Chen, Fang and Shao considered a similar problem for non-critical model by using Stein method. By direct and simple arguments based on Laplace method, we provide an explicit formula of the error and deduce a Cramer-type result.
We establish a central limit theorem and prove a moderate deviation principle for inviscid stochastic Burgers equation. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and doubling variables method play a key role.
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