Invariant Measure for Linear Stochastic PDEs in the space of Tempered distributions

2024/05/30 by Nath, Arvind Kumar
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2405.19926

Abstract

In this paper, we first explore exponential stability by using Monotonicity inequality and use this information to obtain the existence of Invariant measure for linear Stochastic PDEs with potential in the space of tempered distributions. The uniqueness of Invariant Measure follows from Monotonicity inequality.

Related

• Invariant measures for stochastic functional differential equations
• Invariant Measure for Stochastic Functional Differential Equations in Hilbert Spaces
• New Approaches to the Monotonicity Inequality for Linear Stochastic PDEs
• Ergodicity for a class of semilinear stochastic partial differential equations
• Weak Solutions of SPDEs in the space of Tempered distributions