Difference approximation for equations with interaction

K. M. Kustarova
Theory of Stochastic Processes
Vol.29 (45), no.1, 2025, pp.52-64
This paper investigates stochastic differential equations with interaction, introduced by Dorogovtsev the model of the evolution of large systems of interacting particles in random environments. The study emphasizes the difference approximation scheme for these equations, which involve approximating solutions in an infinite-dimensional, nonlinear space of measures. The key contributions include the formulation of approximation schemes for compactly supported initial measures, the derivation of Wasserstein distance-based estimates, and spatial discretization techniques.
DOI: https://doi.org/10.3842/tsp-5123020117-84
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