Comparison theorem of 1-dimensional stochastic hybrid systems
نویسندگان
چکیده
In this paper, the comparison theorem of stochastic differential delay equations with Markovian switching has been investigated. In order to develop our theory, a new proof of existence and uniqueness of stochastic differential equations with Markovian switching is given.
منابع مشابه
Stability analysis of nonlinear hybrid delayed systems described by impulsive fuzzy differential equations
In this paper we introduce some stability criteria of nonlinear hybrid systems with time delay described by impulsive hybrid fuzzy system of differential equations. Firstly, a comparison principle for fuzzy differential system based on a notion of upper quasi-monotone nondecreasing is presented. Here, for stability analysis of fuzzy dynamical systems, vector Lyapunov-like functions are defined....
متن کاملRandom differential inequalities and comparison principles for nonlinear hybrid random differential equations
In this paper, some basic results concerning strict, nonstrict inequalities, local existence theorem and differential inequalities have been proved for an IVP of first order hybrid random differential equations with the linear perturbation of second type. A comparison theorem is proved and applied to prove the uniqueness of random solution for the considered perturbed random differential eq...
متن کاملOn the Hamiltonian structure of large deviations in stochastic hybrid systems
We develop the connection between large deviation theory and more applied approaches to stochastic hybrid systems by highlighting a common underlying Hamiltonian structure. A stochastic hybrid system involves the coupling between a piecewise deterministic dynamical system in Rd and a time-homogeneous Markov chain on some discrete space Γ. We assume that the Markov chain on Γ is ergodic, and tha...
متن کاملUniqueness of Constrained Viscosity Solutions in Hybrid Control Systems
We study constrained viscosity solutions with an unbounded growth for a class of first order Hamilton–Jacobi–Bellman equations arising in hybrid control systems. To deal with the boundary constraint and rapid growth of the solutions, we construct a particular set of test functions and under very mild conditions establish a comparison theorem which gives the estimate of distance between the subs...
متن کاملSymbolic Models for Retarded Jump-Diffusion Systems
In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic hybrid systems, namely, hybrid stochastic retarded systems. First, we construct finite dimensional abstractions approximately bisimilar to original infinite dimensional stochastic systems having some stability property, namely, incrementa...
متن کامل