Analysis of Nonlinear Stochastic Systems with Jumps Generated by Erlang Flow of Events

Alexander S. Kozhevnikov, Konstantin A. Rybakov

Department of Mathematical Cybernetics, Moscow Aviation Institute, Moscow, Russia.

DOI: 10.4236/ojapps.2013.31001                

Abstract

In this paper we consider the stochastic systems with jumps (random impulses) generated by Erlang flow of events that lead to discontinuities in paths. These systems may be used in various applications such as a control of complex technical systems, financial mathematics, mathematical biology and medicine. We propose to use a spectral method formalism to the probabilistic analysis problem for the stochastic systems with jumps. This method allows to get a solution of the analysis problem in an explicit form.

Keywords

Analysis; Erlang Flow of Events; Generalized Fokker-Planck Equations; Random Impulses; Jump-Diffusion Process; Spectral Characteristic; Spectral Method Formalism; Stochastic System

Conflicts of Interest

The authors declare no conflicts of interest.

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