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Quantum systems of interest are typically coupled to several quantum channels (more generally environments). In this paper, we develop an exact stochastic Schrödinger equation for an open quantum system coupled to a hybrid environment containing both bosonic and fermionic particles. Such a stochastic differential equation may be obtained directly from a microscopic model through employing a cla...

We derive a Feynman-Kac formula for functionals of a stochastic hybrid system evolving according to a piecewise deterministic Markov process. We first derive a stochastic Liouville equation for the moment generator of the stochastic functional, given a particular realization of the underlying discrete Markov process; the latter generates transitions between different dynamical equations for the...

This paper discusses exponential stability of solutions for highly nonlinear hybrid pantograph stochastic differential equations(PSDEs). Two criteria are proposed to guarantee exponential stability of the solution. The first criterion is a Khasminskii-type condition involving general Lyapunov functions. The second is developed on coefficients of the equation in virtue of M-matrix techniques. Ba...

In this paper we consider a class of hybrid stochastic games with the piecewise openloop information structure. These games are indexed over a parameter ε which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic ...

A hybrid automaton [16,2] is a digital, real-time system that interacts with an analogue environment. Hybrid automata are ubiquitous in all areas of modern engineering and technology. For example, the (digital) height control of an automobile chassis depends on and influences the (continuous) driving conditions of the vehicle [22]. Hybrid automata typically operate in safety critical areas, suc...

in this paper we apply hybrid functions of general block-pulse‎ ‎functions and legendre polynomials for solving linear and‎ ‎nonlinear multi-order fractional differential equations (fdes)‎. ‎our approach is based on incorporating operational matrices of‎ ‎fdes with hybrid functions that reduces the fdes problems to‎ ‎the solution of algebraic systems‎. ‎error estimate that verifies a‎ ‎converge...