Stochastic Stability of Vector Sde With Applications to a Stochastic Epidemic Model

Abstract

In this paper we consider stochastic stability, namely, asymptotic stability in mean, asymptotic mean-square stability, asymptotic stability a.s., exponential p-stability and stability with stochastic Lyapunov fucntion for vector stochastic differential equations. We apply these results to the stochastic epidemic models induced by bacteriophages in the marine bacteria populations. The novelty of the paper consists of new stability results for vector SDE and their applications to a new stochastic epidemic model.

Hedging and utility valuation of a defaultable claim driven by Hawkes processes

“…(A) Against 𝜆 (1) 0 ; (B) against 𝜆 (3) 0 ; (C) against 𝛼 11 ; (D) against 𝛼 12 in mean, asymptotic mean-square stability, asymptotic stability almost surely and exponential p-stability. Furthermore, an interesting task could be to investigate stability for vector of stochastic differential delay equations with jumps and Markov switchings for financial models when the underlying dynamics are driven by Hawkes processes (see Swishchuk and Kazmerchuk 37 and Swishchuk et al 38 for similar studies based on Poisson jumps).…”

Discrete-Time Semi-Markov Random Evolutions in Asymptotic Reduced Random Media with Applications

“…Useful results in Banach space can be found in, for example, References [14,[34][35][36][37][38][39]. For applications to real problems of the type of results presented here see, for example, References [4,16,[40][41][42].…”