16 research outputs found
Levy Approximation of Impulsive Recurrent Process with Semi-Markov Switching
In this paper, the weak convergence of impulsive recurrent process with
semi-Markov switching in the scheme of Levy approximation is proved. Singular
perturbation problem for the compensating operator of the extended Markov
renewal process is used to prove the relative compactness
Equilibrium in Wright-Fisher models of population genetics
For multivariant Wright-Fisher models in population genetics, we introduce
equilibrium states, expressed by fluctuations of probability ratio, in contrast
to the traditionally used fluctuations, expressed by the difference between the
current value of the random process and its equilibrium value. Then the drift
component of the dynamic process of gene frequencies, primarily expressed as a
ratio of two quadratic forms, is transformed into a cubic parabola with a
certain normalization factor.Comment: 6 pages, a genetic Wright-Fisher model is considered as a
multivariate statistical experiment which has a representation as a Discrete
Markov Diffusio
Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach
AbstractIn this Note, we present the weak convergence of additive functionals of processes with locally independent increments and Markov switching in Lévy and Poisson approximation schemes. The singular perturbation problem for the generators of switched processes is used to prove the semimartingales' predictable characteristics convergence
Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach
AbstractIn this Note, we present the weak convergence of additive functionals of processes with locally independent increments and Markov switching in Lévy and Poisson approximation schemes. The singular perturbation problem for the generators of switched processes is used to prove the semimartingales' predictable characteristics convergence