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On the notion of Markov–up processes

P. 219–223.
Veretennikov A., Veretennikova M.

A new notion of ``Markov up'' processes is discussed. A toy model of this notion is proposed and discussed; recurrence and ergodic properties are studied.

Language: English
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Keywords: positive recurrenceположительная возвратностьMarkov-up processМарковский вверх процесс
Publication based on the results of:
Methods development of the fractional stochastic calculus (2020)

In book

Сборник материалов V-й Международной конференции по стохастическим методам: The 5th International Conference on Stochastic Methods (ICSM5). 23-27 November 2020, Russia, Moscow.
M.: RUDN, 2020.
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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 ...
Added: July 16, 2026
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On positive recurrence of 1D diffusions with switching
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Positive recurrence of one-dimensional diffusion with switching with an additive Wiener process and with one recurrent and one transient regime is established under suitable conditions on the drift in both regimes and on the intensities of switching. ...
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Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the model is proved; the rate of convergence towards this distribution may be theoretically evaluated on the basis of the ...
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