16 citations · 34 across the 9 of their papers we have counts for
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math.PR2021
Piecewise linear processes with Poisson-modulated exponential switching times
Antonio Di Crescenzo, Barbara Martinucci, Nikita Ratanov
We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this proces…
math.PR2021
First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes
Nikita Ratanov
In this paper, we study Ornstein-Uhlenbeck processes with Markov modulation, whose parameters depend on an external underlying two-state Markov process. Conditional mean and varian…
math.PR2021
On telegraph processes, their first passage times and running extrema
Nikita Ratanov
In this note, we present some ideas for describing the distributions of the running maximum/minimum, first passage times and telegraphic meanders. Explicit formulae for joint distr…