arXiv subjects

Marianna S. Troeva

Publications and source records attributed to Marianna S. Troeva.

2 recordsLinked to original sources

arXiv2022

Fractional kinetic equations

We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We prove the well-posedness of the resulting new equations and present a probabilistic formula for their solutions. Though our method are quite general, for simplicity we treat in detail only the fractional versions of the interacting diffusions. The paper can be considered as a development of the ideas from the works of Belavkin and Maslov devoted to Markovian (quantum and classical) systems of interacting particles.

math.PR↗

arXiv2021

Abstract McKean-Vlasov and HJB equations, their fractional versions and related forward-backward systems on Riemannian manifolds

We introduce a class of abstract nonlinear fractional pseudo-differential equations in Banach spaces that includes both the Mc-Kean-Vlasov-type equations describing nonlinear Markov processes and the Hamilton-Jacobi-Bellman(HJB)-Isaacs equation of stochastic control and games thus allowing for a unified analysis of these equations. This leads to an effective theory of coupled forward-backward systems (forward McKean-Vlasov evolution and backward HJB-Isaacs evolution) that are central to the modern theory of mean-field games.

math.DS↗