Bally, Vlad Qin, Yifeng

We deal with stochastic differential equations with jumps. In order to obtain an accurate approximation scheme, it is usual to replace the "small jumps" by a Brownian motion. In this paper, we prove that for every fixed time $t$, the approximate random variable $X^\varepsilon_t$ converges to the original random variable $X_t$ in total variation dis...

Garino, Valentin

We use recent tools from stochastic analysis (such as Stein's method and Malliavin calculus) to study the asymptotic behaviour of some functionals of a Gaussien Field.

Nersesyan, Vahagn Peng, Xuhui Xu, Lihu

The purpose of this paper is to establish the Donsker-Varadhan type large deviations principle (LDP) for the two-dimensional stochastic Navier-Stokes system. The main novelty is that the noise is assumed to be highly degenerate in the Fourier space. The proof is carried out by using a criterion for the LDP developed in [JNPS18] in a discrete-time s...

Guo, Rui Gao, Han Jin, Yang Yan, Litan
Published in
Frontiers in Physics

In this study, as a continuation to the studies of the self-interaction diffusion driven by subfractional Brownian motion S H , we analyze the asymptotic behavior of the linear self-attracting diffusion: d X t H = d S t H − θ ∫ 0 t ( X t H − X s H ) d s d t + ν d t , X 0 H = 0 , where θ > 0 and ν ∈ R are two parameters. When θ

Chen, Xia Deya, Aurélien Song, Jian Tindel, Samy

This paper is concerned with a wave equation in dimension d ∈ {1, 2, 3}, with a multiplicative space-time Gaussian noise which is fractional in time and homogeneous in space. We provide necessary and sufficient conditions on the space-time covariance of the Gaussian noise, allowing the existence and uniqueness of a mild Skorohod solution.

Jafari, Hossein
Published in
Russian Mathematics

In this paper, a class of anticipating stochastic differential equation is considered, where the integrand processes are not adapted to the filtration generated by a Wiener process. Using the correspondence between the Skorohod integral and the Itô–Skorohod integral, the equations can be solved by using standard iterative techniques. The existence ...

Hillairet, Caroline Réveillac, Anthony Rosenbaum, Mathieu

In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the wellknown integration by parts formula (or more precisely the Mecke formula) for Poisson functional. Our approach allows us to provide an expansion of the premium of a class of cyb...

Clarke De La Cerda, Jorge Olivera, Christian Tudor, Ciprian

We analyze the transport equation driven by a zero quadratic variation process. Using the stochastic calculus via regularization and the Malliavin calculus techniques, we prove the existence, uniqueness and absolute continuity of the law of the solution. As an example, we discuss the case when the noise is a Hermite process.

Besançon, Eustache

In many fields of interest, Markov processes are a primary modelisation tool for random processes. Unfortunately it is often necessary to use very large or even infinite dimension state spaces, making the exact analysis of the various characteristics of interest (stability, stationary law, hitting times of certain domains, etc.) of the process diff...

Knani, H Dozzi, M

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaus-sian Volterra processes are given. These processes include the multifractional brownian motion and the mul-tifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a line...