Böcker av Richard Durrett

In its revised new edition, this book covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales and mathematical finance. Offers many examples and more than 300 carefully chosen exercises for better understanding.

This volume develops results on continuous time branching processes and applies them to study rate of tumor growth, extending classic work on the Luria-Delbruck distribution. As applications, the author evaluate ovarian cancer screening strategies and give rigorous proofs for results of Heano and Michor concerning tumor metastasis.

This book presents mathematical techniques for understanding sequence evolution. The theory is developed in close connection with data from more than 60 experimental studies that illustrate the use of these results.

Describes Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. This book solves stochastic differential equations by a variety of methods and studies in detail the one-dimensional case.