Related papers: On a Stochastic Wave Equation Driven by a Non-Gaus…
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed…
The goal of this paper is twofold. In the first part we will study L\'{e}vy white noise in different distributional spaces and solve equations of the type $p(D)s=q(D)\dot{L}$, where $p$ and $q$ are polynomials. Furthermore, we will study…
We investigate the stochastic evolution equations describing the motion of a Non-Newtonian fluids excited by multiplicative noise of L\'evy type. By making use of Galerkin approximation we can prove that the system has a global…
This study aims to examine the effect of L\'evy noise on the solutions of the nonlinear Schr\"odinger equation. An improved diversity of stochastic solutions is instinctively located discretely on certain conditions by applying the…
In this article, well-posedness of stochastic anisotropic $p$-Laplace equation driven by L\'evy noise is shown. Such an equation in deterministic setting was considered by Lions [7]. The results obtained in this article can be applied to…
In this article, we study a nonlinear stochastic control problem perturbed by multiplicative Levy noise, where the nonlinear operator in divergence form satisfies p type growth with coercivity assumptions. By using Aldous tightness criteria…
In this paper we investigate a nonlinear stochastic partial differential equation (spde in short) perturbed by a space-correlated Gaussian noise in arbitrary dimension $d\geq1$, with a non-Lipschitz coefficient noisy term. The equation…
In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…
Large classes of multi-dimensional Gaussian processes can be enhanced with stochastic Levy area(s). In a previous paper, we gave sufficient and essentially necessary conditions, only involving variational properties of the covariance.…
It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models…
We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise. To obtain the existence and uniqueness of strong…
In this paper, based on the white noise analysis of square integrable pure-jump Levy process given by [1], we define the formal derivative of fractional Levy process defined by the square integrable pure-jump Levy process as the fractional…
This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward…
We present a general method to construct couplings of stochastic differential equations driven by L\'{e}vy noise in terms of coupling operators. This approach covers both coupling by reflection and refined basic coupling which are often…
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the…
We consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. We show that for any suitable initial data there exists a pathwise unique, global solution to…
The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of…
Based on the theory of independently scattered random measures, we introduce a natural generalisation of Gaussian space-time white noise to a Levy-type setting, which we call Levy-valued random measures. We determine the subclass of…
Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled…