We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of Markovian regime-switching. first prove existence unique global positive solution, and find invariant set for system. Then, we sufficient conditions a.s. extinction permanence, showing also their relation with stationary probability distribution Markov chain that governs switching netw...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

in this study, a new stochastic model is proposed to deal with a multi-product, multi-period, multi-stage, multi-site production and transportation supply chain planning problem under demand uncertainty. a two-stage stochastic linear programming approach is used to maximize the expected profit. decisions such as the production amount, the inventory level of finished and semi-finished product, t...

We propose an analytically tractable class of models for the dynamics a limit order book, described through stochastic partial differential equation with multiplicative noise book centered at mid-price, along mid-price which is consistent flow dynamics. provide conditions under model admits finite-dimensional realization driven by (low-dimensional) Markov process, leading to efficient methods e...

Biological systems involving genetic reactions are large discrete event systems, and often contain certain species that occur in small quantities, and others that occur in large quantities, leading to a difficulty in modeling and simulation. Small populations inhibit the usefulness of utilizing differential equations to represent the system, while the large populations cause stochastic discrete...