A LARGE DEVIATION PRINCIPLE FOR THE STOCHASTIC GENERALIZED GINZBURG-LANDAU EQUATION DRIVEN BY JUMP NOISE

In this paper,we establish a large deviation principle for the stochastic generalized Ginzburg-Landau equation driven by jump noise.The main difficulties come from the highly non-linear coefficient and the jump noise.Here,we adopt a new sufficient condition for the weak convergence criterion of the large deviation principle,which was initially proposed by Matoussi,Sabbagh and Zhang(2021).

Ito Formula for Integral Processes Related to Space-Time Levy Noise

In this article, we give a new proof of the Itôformula for some integral processes related to the space-time Lévy noise introduced in [1] [2] as an alternative for the Gaussian white noise perturbing an SPDE. We discuss two applications of this result, which are useful in the study of SPDEs driven by a space-time Lévy noise with finite variance: a maximal inequality for the p-th moment of the stochastic integral, and the Itôrepresentation theorem leading to a chaos expansion similar to the Gaussian case.

An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure

This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditions to deal with the averaging principle for Caputo fractional stochastic differential equations.Under these conditions,the solution to a Caputo fractional stochastic differential system can be approximated by that of a corresponding averaging equation in the sense ofmean square.

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH BROWNIAN MOTION AND POISSON PROCESS

Existence and uniqueness results of the solution to fully coupled forward-backward stochastic defferential equations with Brownian motion and Poisson process are obtained. Many stochastic Hamilton systems arising in stochastic optimal control systems with random jump and in mathemstical finance with security price discontinuously changing can be treated with these results. The continuity of the solution depending on parameters is also proved in this paper.

COVID-19: Analytics of contagion on inhomogeneous random social networks

Motivated by the need for robust models of the Covid-19 epidemic that adequately reflect the extreme heterogeneity of humans and society,this paper presents a novel framework that treats a population of N individuals as an inhomogeneous random social network(IRSN).The nodes of the network represent individuals of different types and the edges represent significant social relationships.An epidemic is pictured as a contagion process that develops day by day,triggered by a seed infection introduced into the population on day 0.Individuals’social behaviour and health status are assumed to vary randomly within each type,with probability distributions that vary with their type.A formulation and analysis is given for a SEIR(susceptible-exposed-infective-removed)network contagion model,considered as an agent based model,which focusses on the number of people of each type in each compartment each day.The main result is an analytical formula valid in the large N limit for the stochastic state of the system on day t in terms of the initial conditions.The formula involves only one-dimensional integration.The model can be implemented numerically for any number of types by a deterministic algorithm that efficiently incorporates the discrete Fourier transform.While the paper focusses on fundamental properties rather than far ranging applications,a concluding discussion addresses a number of domains,notably public awareness,infectious disease research and public health policy,where the IRSN framework may provide unique insights.

Transportation Cost Inequalities for Stochastic Reaction-Diffusion Equations with Lévy Noises and Non-Lipschitz Reaction Terms

For stochastic reaction-diffusion equations with Levy noises and non-Lipschitz reaction terms,we prove that W\H transportation cost inequalities hold for their invariant probability measures and for their process-level laws on the path space with respect to the L1-metrie.The proofs are based on the Galerkin approximations.

Stochastic Fubini Theorem for Jump Noises in Banach Spaces

We prove a general version of the stochastic Fubini theorem for stochastic integrals of Banach space valued processes with respect to compensated Poisson random measures under weak integrability assumptions, which extends this classical result from Hilbert space setting to Banach space setting.

Moderate deviations for neutral functional stochastic differential equations driven by Levy noises

Using the weak convergence method introduced by A.Budhiraja,P.Dupuis,and A.Ganguly[Ann.Probab.,2016,44:1723-1775],we establish the moderate deviation principle for neutral functional stochastic differential equations driven by both Brownian motions and Poisson random measures.