Asymptotic behavior of the solution to the multi-dimensional stochastic differential equation with interactions
Анотація
This paper explores the asymptotic behavior of solutions to multi-dimensional stochastic differential equations with interactions (SDEWI). By integrating interaction terms reflecting the distribution of all participating particles, SDEWI provides a complex model that captures dynamic changes across a system of particles. Theoretical insights are substantiated by the derivation of conditions under which the solutions exhibit specific asymptotic properties. This work extends previous research by confirming the shift-compactness criterion and establishing conditions for the existence of asymptotic limits, thereby offering a deeper understanding of the interaction dynamics within stochastic systems.
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