Related papers: Multiparameter L\'evy white noise theory and appli…

We study the composition of bivariate L\'evy process with bivariate inverse subordinator. The explicit expressions for its dispersion and auto correlation matrices are obtained. Also, the time-changed two parameter L\'evy processes with…

We identify the representation of the square of white noise obtained by L. Accardi, U. Franz and M. Skeide in [Comm. Math. Phys. 228 (2002), 123--150] with the Jacobi field of a L\'evy process of Meixner's type.

Gradient estimates are derived, for the first time, for the semigroup associated to a class of stochastic differential equations driven by multiplicative L\'evy noise. In particular, the estimates are sharp for $\alpha$-stable type noises.…

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric L\'evy white noise. We identify conditions for existence for these two kinds of solutions,…

We are concerned with multidimensional stochastic balance laws driven by L\'{e}vy processes. Using bounded variation (BV) estimates for vanishing viscosity approximations, we derive an explicit continuous dependence estimate on the…

The problem of distributed estimation of a parametric physical field is stated as a maximum likelihood estimation problem. Sensor observations are distorted by additive white Gaussian noise. Prior to data transmission, each sensor quantizes…

This paper studies the behaviour of quadratic variations of a stochastic wave equation driven by a noise that is white in space and fractional in time. Complementing the analysis of quadratic variations in the space component carried out by…

Covariant stochastic partial differential equations are studied in any dimension. A special class of such equations is selected and it is proven that the solutions can be analytically continued to Minkowski space-time yielding tempered…

In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…

In this paper, we study almost periodic solutions for semilinear stochastic differential equations driven by L\'{e}vy noise with exponential dichotomy property. Under suitable conditions on the coefficients, we obtain the existence and…

Non-Gaussian impulsive noise (IN) with memory exists in many practical applications. When it is mixed with white Gaussian noise (WGN), the resultant mixed noise will be bursty. The performance of communication systems will degrade…

Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…

In this paper we focus on the stochastic Euler-Poincar\'{e} equations with pseudo-differential/multiplicative noise. We first establish two new cancellation properties on pseudo-differential operators, which play a key role in energy…

Multivariate Poisson random variables subject to linear integer constraints arise in several application areas, such as queuing and biomolecular networks. This note shows how to compute conditional statistics in this context, by employing…

This article generalizes the small noise cutoff phenomenon to the strong solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain subject to additive and multiplicative Wiener and L\'evy noises…

We investigate a class of stochastic integro differential equations driven by Levy noise.

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an…

We consider the concepts of continuous Bernoulli systems and non-commutative white noises. We address the question of isomorphism of continuous Bernoulli systems and show that for large classes of quantum L{\'e}vy processes one can make…

In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) L\'{e}vy noise taking values in the dual of a nuclear space. As part of our approach…

This paper investigates a damped stochastic wave equation driven by a non-Gaussian Levy noise. The weak solution is proved to exist and be unique. Moreover we show the existence of a unique invariant measure associated with the transition…