On Exponential Recurrence of "Markov-up'' Processes

D.O. Kalikaeva

2023, v.29, Issue 2, 225-240


This paper continues developing the theory of ``Markov-up'' processes. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and is described in technical literature, for instance \cite{IE}, \cite{M9}. Naturally, phenomena of this type require special mathematical models. This paper follows the proposal of such a model published recently in \cite{VV22} where the authors focus on the issue of recurrence and positive recurrence. In this article exponential recurrence of the same process is established under appropriate assumptions, which potentially leads to an exponential rate of convergence to the invariant measure.

Keywords: Markov-up process; recurrence; exponential moment


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