الصفحة 1
الصفحة 1
Interacting particle systems
This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years.The first monographic presentation of this important and rapidly developing theory.
Free Energy and Self-Interacting Particles
This book examines a system of parabolic-elliptic partial differential eq- tions proposed in mathematical biology, statistical mechanics, and chemical kinetics. In the context of biology, this system of equations describes the chemotactic feature of cellular slime molds and also the capillary formation of blood vessels in angiogenesis. There are several methods to derive this system. One is the biased random walk of the individual, and another is the reinforced random walk of one particle modelled on the cellular automaton. In the context of statistical mechanics or chemical kinetics, this system of equations describes the motion of a mean field of many particles, interacting under the gravitational inner force or the chemical reaction
An Introduction to continuous-time stochastic processes : Theory, models, and applications to finance, biology, and medicine
This book is introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required. Key topics covered include: * Interacting particles and agent-based models: from polymers to ants * Population dynamics: from birth and death processes to epidemics * Financial market models: the non-arbitrage principle * Contingent claim valuation models: the risk-neutral valuation theory * Risk analysis in insurance
