arXiv subjects

Tijana Levajković

Publications and source records attributed to Tijana Levajković.

4 recordsLinked to original sources

arXiv2025

Stochastic very weak solution to parabolic equations with singular coefficients

A class of stochastic parabolic equations with singular potentials is analysed in the chaos expansion setting where the Wick product is used to give sense to the product of generalized stochastic processes. For the analysis of such equations we combine the chaos expansion method from the white noise analysis and the concept of very weak solutions from the theory of partial differential equations. The stochastic very weak solution to the stochastic parabolic evolution problem is defined and its existence and uniqueness are shown. For regular enough potentials and data we prove consistency of stochastic very weak solution with a stochastic weak solution. We give an example to illustrate the method and possible applications.

math.AP↗

arXiv2022

Wick-type stochastic parabolic equations with random potentials

The stochastic parabolic equations with random potentials, driving forces and initial conditions are considered. The Wick product is used to give sense to the product of two generalized stochastic processes, and the existence and uniqueness of solutions are proved via the chaos expansion method from white noise analysis. The estimates on coefficients in the chaos expansion form of the solutions are provided.

math.PR↗

arXiv2021

Stochastic parabolic equations with singular potentials

In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from the white noise analysis and the concept of very weak solutions. For given stochastic parabolic equation we introduce the notion of a stochastic very weak solution, prove the existence and uniqueness of the very weak solution to corresponding stochastic initial value problem and show its independence of a regularization on given singular potential. In addition, the consistency of a stochastic very weak solution with a stochastic weak solution is shown.

math.AP↗

arXiv2019

A splitting/polynomial chaos expansion approach for stochastic evolution equations

In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve explicitly by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach.

math.NA↗