Brownian Dynamics at Boundaries and Interfaces

The Mathematical Brownian Motion.- Euler Simulation of Ito SDEs.- Simulation of the Overdamped Langevin Equation.- The First Passage Time of a Diffusion Process.- Chemical Reaction in Microdomains.- The Stochastic Separatrix.- Narrow Escape in R2.- Narrow Escape in R3.

Zeev Schuss is a Professor at Tel Aviv University.

From the book reviews:

"This text provides an excellent entry point for applied mathematicians who would like to get a first understanding of the field of neuronal modeling, with a bold motivation and immediate application to highly relevant phenomena in the science ... . this text may serve as an excellent basis for a specialized course on neuronal modeling or biophysics at master's level and as a common reference text for interdisciplinary teams, which perfectly reflects the author's long working experience." (P. R. C. Ruffino, zbMATH, Vol. 1305, 2015)

"This book uniquely combines an introduction to the mathematical theory of Brownian motion with applications to chemical kinetics, primarily in biology and physiology. ... this a unique and valuable book. ... Exercises are included throughout the book, particularly relating to the mathematical theory. The book will be extremely useful to both mathematicians and biologists/physiologists, etc., who work at the interface of these two subjects." (D. J. W. Simpson, SIAM Review, Vol. 56 (4), December, 2014)"This book will be of interest to a broad group of students and researchers. It presents a style of analysis that is typical of applications in physics and applied sciences-an explicit transition-density style based on the Fokker-Planck and Langevin equations, and the forward Kolmogorov equation, and defining solutions to stochastic differential equations through the Euler scheme of successive approximations ... ." (David R. Steinsaltz, Mathematical Reviews, November, 2014)