16 citations · 34 across the 9 of their papers we have counts for
11 papers
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…
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…
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…
Ornstein-Uhlenbeck processes of bounded variation
Nikita Ratanov
Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion…
Kac-Lévy processes
Nikita Ratanov
Markov-modulated Lévy processes with two different regimes of restarting are studied. These regimes correspond to the completely renewed process and to the process of Markov modula…
On jump-diffusion processes with regime switching: martingale approach
Antonio Di Crescenzo, Nikita Ratanov
We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these proc…