Invariant measure for neutral stochastic functional differential equations with non-Lipschitz coefficients
Andriy Stanzhytsky, Oleksandr Misiats, Oleksandr Stanzhytskyi
Abstract
<p style='text-indent:20px;'>In this work we study the long time behavior of nonlinear stochastic functional-differential equations of neutral type in Hilbert spaces with non-Lipschitz nonlinearities. We establish the existence of invariant measures in the shift spaces for such equations. Our approach is based on Krylov-Bogoliubov theorem on the tightness of the family of measures.</p>
Topics & Concepts
Lipschitz continuityMathematicsInvariant measureInvariant (physics)Nonlinear systemHilbert spaceStochastic differential equationMathematical analysisDifferential equationPure mathematicsMeasure (data warehouse)Mathematical physicsPhysicsComputer scienceErgodic theoryDatabaseQuantum mechanicsStability and Controllability of Differential EquationsStochastic processes and financial applicationsAdvanced Mathematical Modeling in Engineering