Zeev Schuss

Theory and Applications of Stochastic Differential Equations

Presents theory, sources, and applications of stochastic differential equations of Itos type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.

The Exit Problem for Randomly Perturbed Dynamical Systems

The cumulative effect on dynamical systems, of even very small random perturbations, may be considerable after sufficiently long times. For example, even if the corresponding deterministic system has an asymptotically stable equilibrium point, random effects can cause the trajectories of the system to leave any bounded domain with probability one. In this paper we consider the effect of small random perturbations of the type referred to as Gaussian white noise, on a (deterministic) dynamical system

Time scale of diffusion in molecular and cellular biology

\dot x = b(x)

A direct approach to the exit problem

. The vector

DIFFUSION AS A CHEMICAL REACTION : STOCHASTIC TRAJECTORIES BETWEEN FIXED CONCENTRATIONS

x(t)

Singular Perturbation Methods in Stochastic Differential Equations of Mathematical Physics

then becomes a stochastic process

AN ASYMPTOTIC THEORY OF LARGE DEVIATIONS FOR MARKOV JUMP PROCESSES

x_\varepsilon (t)

A SINGULAR PERTURBATION APPROACH TO KRAMERS' DIFFUSION PROBLEM*

which satisfies the stochastic differential equation

Diffusion theory of multidimensional activated rate processes: The role of anisotropy

dx_\varepsilon = b(x_\varepsilon )dt + \varepsilon \sigma (x_\varepsilon )dw

A subjective Bayesian approach to the theory of queues II—Inference and information in M/M/1 queues

. Here