This work focuses on analyzing and presenting solutions for a wide
range of stochastic problems that are encountered in applied
mathematics, probability, physics, engineering, finance, and
economics. The approach used reduces the gap between the
mathematical and engineering literature. Stochastic problems are
defined by algebraic, differential or integral equations with
random coefficients and/or input. However, it is the type, rather
than the particular field of application, that is used to
categorize these problems.
An introductory chapter outlines the types of stochastic
problems under consideration in this book and illustrates some of
their applications. A user friendly, systematic exposition unfolds
as follows: The essentials of probability theory, random processes,
stochastic integration, and Monte Carlo simulation are developed in
chapters 2--5. The Monte Carlo method is used extensively to
illustrate difficult theoretical concepts and solve numerically
some of the stochastic problems in chapters 6--9.
Key features:
* Computational skills developed as needed to solve realistic
stochastic problems
* Classical mathematical notation used, and essential
theoretical facts boxed
* Numerous examples from applied sciences and engineering
* Complete proofs given; if too technical, notes clarify the
idea and/or main steps
* Problems at the end of each chapter reinforce applications;
hints given.
* Good bibliography at the end of every chapter
* Comprehensive index
This work is unique, self-contained, and far from a collection
of facts and formulas. The analytical and numerical methods
approach for solving stochastic problems may be used for self-study
by avariety of researchers, and in the classroom by first year
graduate students.
General
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