文档介绍：A
A B
k
B +
∂∂p()xt,,2 p() xt
=
D 2 k− C
∂∂tx C
Applied Stochastic
Processes
in science and engineering
by
M. Scott
⃝c 2012
Objectives
This book is designed as an introduction to the ideas and methods used to
formulate mathematical models of physical processes in terms of random
functions. The first five chapters use the historical development of the
study of Brownian motion as their guiding narrative. The remaining
chapters are devoted to methods of solution for stochastic models. The
material is too much for a single course – chapters 1-4 along with chapters
7 and 8 are ample for a senior undergraduate course offered to students
with a suitably mathematical background (. familiarity with most of
the methods reviewed in Appendix B). For a graduate course, on the
other hand, a quick review of the first three chapters, with a focus on
later chapters should provide a good general introduction to numerical
and analytic approximation methods in the solution of stochastic models.
The content is primarily designed to develop mathematical methods
useful in the study of stochastic processes. Nevertheless, an effort has been
made to tie the derivations, whenever possible, to the underlying physical
assumptions that gave rise to the mathematics. As a consequence, very
littleissaidaboutItˆo formula and associated methods of what e
to be called Stochastic Calculus. If es as a disappointment to the
reader, I suggest they consider C. W. Gardiner’s book:
∙ Handbook of stochastic methods (3rd Ed.), C. W. Gardiner (Springer,
2004),
as a friendly introduction to Itˆo’s calculus.
A list of references useful for further study appear at the beginning
of some sections, and at the end of each chapter. These references are
usually pedagogical texts or review articles, and are not meant to be an
exhaustive tabulation of current results, but rather as a first step along
the road of independent research in stochastic processes. A collectio