2013/03/12 by Nikita Ratanov, Ratanov, Nikita
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1303.2796
openalex publication_date 2013/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a one-dimensional Markov modulated random walk with jumps. It is assumed that amplitudes of jumps as well as a chosen velocity regime are random and depend on a time spent by the process at a previous state of the underlying Markov process. Equations for the distribution and equations for its moments are derived. We characterise the martingale distributions in terms of observable proportions between jump and velocity regimes.