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.
Describes Brownian motion and the associated stochastic calculus, including their relationship to partial differential equations. This book solves sto...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approa...
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatorial probability and Markov chains. Concise and focused, it is designed for a one-semester introductory course in probability for students who have some familiarity with basic calculus. Reflecting the author s philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. The examples contain all the old standards such as the birthday problem and Monty Hall, but also include a number of...
This clear and lively introduction to probability theory concentrates on the results that are the most useful for applications, including combinatoria...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approach this question we introduce and analyze a number of probability models: the Wright-Fisher model, the coalescent, the infinite alleles model, and the infinite sites model. We study the complications that come from nonconstant population size, recombination, population subdivision, and three forms of natural selection: directional selection, balancing selection, and background selection. These theoretical results set the stage for the...
Our basic question is: Given a collection of DNA sequences, what underlying forces are responsible for the observed patterns of variability? To approa...
This book contains two of the three lectures given at the Saint-Flour Summer School of Probability Theory during the period August 18 to September 4, 1993.
This book contains two of the three lectures given at the Saint-Flour Summer School of Probability Theory during the period August 18 to September 4, ...
This test is designed for a Master's Level course in stochastic processes. It features the introduction and use of martingales, which allow one to do much more with Brownian motion, e.g., option pricing, and queueing theory is integrated into the Continuous Time Markov Chain and Renewal Theory chapters as examples.
This test is designed for a Master's Level course in stochastic processes. It features the introduction and use of martingales, which allow one to do ...
These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. In this contribution the author uses multitype branching processes with mutation to model cancer. With cancer progression, resistance to therapy, the time of the first type $k$ mutation, and $sigma_k$, the time of the first type $k$ mutation that founds a family line that does not die out, as well as the growth of the number of type $k$ cells. The last three sections apply these results to metastasis, ovarian cancer, and tumor heterogeneity. Even...
These notes originated as part of a lecture series on Stochastics in Biological Systems at the Mathematical Biosciences Institute in Ohio, USA. In ...
