Related papers: A Complete Decomposition of Stochastic Differentia…
We develop an efficient numerical scheme for the 3D mean-field spherical dynamo equation. The scheme is based on a semi-implicit discretization in time and a spectral method in space based on the divergence-free spherical harmonic…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
Existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise is proved. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear…
This paper studies the convergence of three temporal semi-discretizations for a backward semilinear stochastic evolution equation. For general terminal value and general coefficient with Lipschitz continuity, the convergence of the first…
By analogue of [1,2] we define a cubic stochastic process and study evolution (dynamics) of a system $E$ which contains at least three elements.
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
We develop a family of reformulations of an arbitrary consistent linear system into a stochastic problem. The reformulations are governed by two user-defined parameters: a positive definite matrix defining a norm, and an arbitrary discrete…
Singular limits of a class of evolutionary systems of partial differential equations having two small parameters and hence three time scales are considered. Under appropriate conditions solutions are shown to exist and remain uniformly…
A Milstein-type method is proposed for some highly non-linear non-autonomous time-changed stochastic differential equations (SDEs). The spatial variables in the coefficients of the time-changed SDEs satisfy the super-linear growth condition…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a…
In this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad-graph by the multiple scale reduction around their harmonic solution. We show that the A_1, A_2 and A_3 linearizability…
In this paper we present the theoretical framework needed to justify the use of a kernel-based collocation method (meshfree approximation method) to estimate the solution of high-dimensional stochastic partial differential equations…
This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation…
We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3-spheres. Besides the main ideas, we discuss issues related to our…
In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional…
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unknowns…
A new notion of stochastic transformation is proposed and applied to the study of both weak and strong symmetries of stochastic differential equations (SDEs). The correspondence between an algebra of weak symmetries for a given SDE and an…
Given a matrix of distribution functions and a quasi-stochastic matrix, i.e. an irreducible nonnegative matrix with maximal eigenvalue one and associated unique positive left and right eigenvectors, the article studies the properties of an…