This research aims to investigate a boundary-value problem for a parabolic equation influenced by a stochastic measure.
Studied the effects of sigma-additivity on solutions to the parabolic equation.
Analyzed the continuity properties of the solutions, specifically focusing on Hölder continuity.
Utilized mathematical techniques to prove results regarding the solution's behavior.
Demonstrated that the solution of the parabolic equation exhibited Hölder continuity.
Provided insights on the implications of sigma-additivity in the context of stochastic measures.
Abstract
A boundary-value problem for a parabolic equation driven by a stochastic measure μ, for which only its σ -additivity is assumed, is studied. The Hölder continuity of the solution of the equation is proved.