Books in the Advanced Series on Statistical Science & Applied Probability series

Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary.

Valuation and hedging of financial derivatives are intrinsically linked concepts. Choosing appropriate hedging techniques depends on both the type of derivative and assumptions placed on the underlying stochastic process. This title provides a systematic treatment of hedging in incomplete markets.

Provides a variety of important results and examples of Markov processes, random measures, stable distributions, Ising ferromagnets, interacting particle systems, stochastic differential equations, random graphs and other models.

This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, Laws of Large Numbers, interactions and random media.Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well.The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

In this book, an integrated introduction to statistical inference is provided from a frequentist likelihood-based viewpoint. Classical results are presented together with recent developments, largely built upon ideas due to R.A. Fisher. The term "neo-Fisherian" highlights this.

Offers a comprehensive treatment of the classical and modern ruin probability theory. This title includes topics such as: Lundberg's inequality, the Cramer-Lundberg approximation, exact solutions, other approximations, finite horizon ruin probabilities, and extensions of the classical compound Poisson model to allow for reserve-dependent premiums.