Books in the Stochastic Modelling and Applied Probability series

This volume provides an introduction to stochastic differential equations with jumps, in both theory and application. The book is accessible and contains many new results on numerical methods but also innovative methodologies in quantitative finance.

The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes.

This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged.

Shortly after the end of World War II high-speed digital computing machines were being developed. We discovered, for example, that even Gaus sian elimination was not well understood from a machine point of view and that no effective machine oriented elimination algorithm had been developed.

The book deals mainly with three problems involving Gaussian stationary processes. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.

This book provides a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods.

This book is an introduction to optimal stochastic control for continuous time Markov processes and the theory of viscosity solutions. New chapters in this second edition introduce the role of stochastic optimal control in portfolio optimization and in pricing derivatives in incomplete markets and two-controller, zero-sum differential games.

As more applications are found, interest in Hidden Markov Models continues to grow.

Stochastic control is a very active area of research. This monograph, written by two leading authorities in the field, has been updated to reflect the latest developments. It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development.

This book on mathematical, statistical and stochastic models in reliability will help analysts formulate general failure models, establish formulae for computing performance measures, and determine how to identify optimal replacement policies.

This thoroughly revised second edition includes a brand new chapter devoted to volatility risk. As a consequence, hedging of plain-vanilla options and valuation of exotic options are no longer limited to the Black-Scholes framework with constant volatility.

In insurance and finance applications, questions involving extremal events play an important role. This book sets out to bridge the gap between existing theory and practical applications both from a probabilistic as well as statistical point of view.

The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences.The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations.

BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis.

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations.