Invariant Sample Measures for Non-autonomous Stochastic Non-local Discrete p-Laplacian Equations with Time Varying Delay and Multiplicative Noises

Abstract

In this article, a class of non-local stochastic lattice models with fractional powers of the discrete p-Laplacian, incorporating time-varying-distributed delay as well as multiplicative noises at each node, are propounded. First, by utilizing an existence theorem of solutions for infinite ordinary differential equations, we prove the well-posedness of the stochastic equations, whose solution operator admits an NRDS. Besides, the tempered random attractor is constructed for this NRDS. Finally, with the identical conditions, we prove that the solution is jointly continuous in initial time and initial data, and eventually, a family of invariant sample Borel probability measures supported in the random attractors are established in a Banach space (not a Hilbert space) for the corresponding NRDS.