Moscow Mathematical Journal

Volume 24, Issue 1, January–March 2024 pp. 107–124.

On Higher Order Moments and Rates of Convergence for SDEs with Switching

Authors: Alexander Veretennikov (1)
Author institution:(1) Institute for Information Transmission Problems, Moscow, Russia

Summary:

Second order recurrence are established for a $d$-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities, under suitable conditions. As a corollary, the rate of convergence towards the invariant regime of order $t^{-2}$ is claimed. The approach is based on embedded Markov chains and a priori bounds for the moments of the diffusion component at times of jumps of the discrete component, as well as on certain simple martingale properties.

2020 Math. Subj. Class. 60H10, 60J60.

Keywords: Diffusion, switching, positive recurrence, 2-recurrence.

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