In this paper we consider large state space continuous time Markov chains arising in the field of systems biology. For a class of such models, namely, for density dependent families of Markov chains that model the interaction of large groups of identical objects, Kurtz has proposed two kinds of approximations. One is based on ordinary differential equations and provides a deterministic approxim...

Calculations of noise-assisted jump rates and diffusion coefficients for diffusion of atoms adsorbed on a metal surface are presented and discussed, in the whole range of the damping strength, and with a direct numerical integration of the Langevin equation, by two different procedures: a mean first passage time calculation and by counting jumps with a given energy criterion. The results are co...

Stochastic hybrid systems arise in numerous applications of systems with multiple models; e.g., air traffc management, flexible manufacturing systems, fault tolerant control systems etc. In a typical hybrid system, the state space is hybrid in the sense that some components take values in a Euclidean space, while some other components are discrete. In this paper we propose two stochastic hybrid...

We propose a model for valuing participating life insurance products under a generalized jumpdiffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regimeswitching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experim...

The Black-Scholes(BS) model has been widely and successfully used to model the return of asset and to price financial options. Despite of its success the basic assumptions of this model, that is, Brownian motion and normal distribution are not always supported by empirical studies. Those studies showed the two empirical phenomena: (1) the asymmetric leptokurtic features, (2) the volatility smil...

A Chapman-Enskog expansion is used to derive hyperbolic models for chemosensitive movements as a hydrodynamic limit of a velocity-jump process. On the one hand, it connects parabolic and hyperbolic chemotaxis models since the former arise as diffusion limits of a similar velocity-jump process. On the other hand, this approach provides a unified framework which includes previous models obtained ...

Most theoretical models for NMR relaxation in liquids assume that overall rotational motion can be described as rotational diffusion with a single diffusion tensor. Such models cannot handle motions (such as between "closed" and "open" states of an enzyme, or between conformers of a partially disordered system) where the shape of the molecule (and hence its rotational diffusion behavior) fluctu...