Introduction to Stochastic Processes, Second EditionCRC Press, 2006. 5. 16. - 248페이지 Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals. |
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VI | 9 |
VII | 14 |
VIII | 17 |
IX | 24 |
X | 26 |
XI | 31 |
XII | 35 |
XIII | 43 |
XLII | 142 |
XLIII | 146 |
XLIV | 149 |
XLV | 153 |
XLVII | 155 |
XLVIII | 160 |
XLIX | 164 |
L | 168 |
XIV | 45 |
XV | 50 |
XVI | 53 |
XVII | 57 |
XVIII | 65 |
XIX | 68 |
XX | 72 |
XXI | 79 |
XXII | 80 |
XXIII | 85 |
XXVI | 91 |
XXVII | 94 |
XXVIII | 96 |
XXIX | 99 |
XXXII | 104 |
XXXIII | 108 |
XXXIV | 112 |
XXXV | 114 |
XXXVI | 120 |
XXXVII | 123 |
XXXVIII | 129 |
XLI | 134 |
LI | 171 |
LIII | 174 |
LIV | 179 |
LV | 182 |
LVI | 187 |
LVII | 189 |
LVIII | 190 |
LIX | 191 |
LX | 193 |
LXI | 197 |
LXIV | 198 |
LXV | 203 |
LXVI | 207 |
LXVII | 214 |
LXVIII | 216 |
LXIX | 219 |
LXX | 221 |
LXXI | 226 |
LXXIII | 227 |
LXXIV | 229 |
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aperiodic assume birth-and-death boundary Brownian motion chain starts compute conditional expectation consider continuous-time Markov chain customer arrives define denote density differential equation discrete-time distribution function eigenvalues eigenvectors Example Exercise expected number exponential finite given gives graph Hence independent random variables infinite invariant probability irreducible Markov chain Itô's formula large numbers law of large Let Xn Markov chain Markov property martingale with respect min{n nonnegative Note number of steps o(At optimal strategy P{Xn P{Xt parameter Poisson process positive recurrent probability distribution probability vector queue real numbers renewal process respect to Fn reversible with respect roll S₁ Show simple random walk solution space standard Brownian motion stochastic differential equation stochastic matrix Stochastic Processes stopping superharmonic Suppose T₁ transient transition matrix transition probabilities uniformly integrable variance write Y₁ μη