Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random...

Randomization has become a standard approach in algorithm design. Efficiency
and simplicity are the main features of randomized algorithms that
often made randomization a miraculous springboard for solving complex problems
in various applications. Especially in the areas of communication, cryptography,
data management, and discrete...

This book is an introduction to modern ideas in cryptology and how to employ
these ideas. It includes the relevant material on number theory, probability, and
abstract algebra, in addition to descriptions of ideas about algorithms and com
plexity theory. Three somewhat different terms appear in the discussion of secure
communications...

Monte Carlo methods are a class of computational algorithms for simulating the behavior of a wide range of various physical and mathematical systems (with many variables). Their utility has increased with general availability of fast computers, and new applications are continually forthcoming. The basic concepts of Monte Carlo are both simple and...

Wallis's book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates...

This book bridges the latest software applications with the benefits of modern resampling techniques

Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques...

This updated text provides a superior introduction to applied probability and statistics for engineering or science majors. Ross emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and...

As the discipline of computer science has matured, it has become clear that a study of discrete mathematical topics is an essential part of the computer science major. The course in discrete structures has two primary aims. The first is to introduce students to the rich mathematical structures that naturally describe much of the content of...

Bayesian networks have received a lot of attention over the last few decades from both scientists and engineers, and across a number of fields, including artificial intelligence (AI), statistics, cognitive science, and philosophy.

Perhaps the largest impact that Bayesian networks have had is on the field of AI, where they were...

Reveals How HMMs Can Be Used as General-Purpose Time Series Models

Implements all methods in R Hidden Markov Models for Time Series: An Introduction Using R applies hidden Markov models (HMMs) to a wide range of time series types, from continuous-valued, circular, and...

Authored by a ranking authority in Gaussian harmonic analysis, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: harmonic analysis and probability. The book is intended for a very diverse audience, from graduate students all the way to researchers working in a...

This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory,...