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20072026
most citedBeware of the Small-World neuroscientist!

65 citations

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9 papers · 1 filter

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.PR2020★ 11 cited

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…

math.PR2018

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…

math.PR2015★ 7 cited

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…

math.PR2015

On the LP formulation in measure spaces of optimal control problems for jump-diffusions

Rafael Serrano

In this short note we formulate a infinite-horizon stochastic optimal control problem for jump-diffusions of Ito-Levy type as a LP problem in a measure space, and prove that the op…

math.PR2013★ 16 cited

Telegraph Processes with Random Jumps and Complete Market Models

Nikita Ratanov

We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spe…