相关论文: A functional non-central limit theorem for jump-di…

Convergence of stochastic processes with jumps to diffusion processes is investigated in the case when the limit process has discontinuous coefficients. An example is given in which the diffusion approximation of a queueing model yields a…

This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other…

A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy…

Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…

Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time…

We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…

We consider functionals of long-range dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the long-range dependence is strong enough, the limit is a Hermite process, while for weaker long-range…

We derive upper estimates of transition densities for Feller semigroups with jump intensities lighter than that of the rotation invariant stable Levy process

In this paper, we study the homogenization of a diffusion process with jumps, that is, Feller process generated by an integro-differential operator. This problem is closely related to the problem of homogenization of boundary value problems…

In this paper, we develop a general law of large numbers and central limit theorem for cumulative reward processes associated with finite state Markov jump processes with non-stationary transition rates. Such models commonly arise in…

We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients when the drift depends on time and space and is periodic in the time argument. There is no time…

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

In this paper we establish a comparison theorem for stochastic differential delay equations with jumps. An example is constructed to demonstrate that the comparison theorem need not hold whenever the diffusion term contains a delay function…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…

In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the…

We present some limit theorems for the normalized laws (with respect to functionals involving last passage times at a given level up to time t) of a large class of null recurrent diffusions. Our results rely on hypotheses on the L\'evy…

We study the stochastic diffusive limit of a kinetic radiative transfer equation, which is non-linear, involving a small parameter and perturbed by a smooth random term. Under an appropriate scaling for the small parameter, using a…

The weak noise limit of dissipative dynamical systems is often the most fascinating one. In such a case fluctuations can interact with a rich complexity frequently hidden in deterministic systems to give rise of completely new phenomena…

Given $n$ equidistant realisations of a L\'evy process $(L_t,\,t\ge 0)$, a natural estimator $\hat N_n$ for the distribution function $N$ of the L\'evy measure is constructed. Under a polynomial decay restriction on the characteristic…