A Probability PathMany probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.
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Contents
II | 1 |
III | 2 |
IV | 5 |
V | 6 |
VI | 8 |
VII | 11 |
VIII | 13 |
IX | 15 |
LXXIV | 219 |
LXXV | 222 |
LXXVI | 226 |
LXXVII | 230 |
LXXVIII | 234 |
LXXIX | 247 |
LXXX | 252 |
LXXXI | 255 |
X | 16 |
XI | 18 |
XII | 20 |
XIII | 29 |
XIV | 35 |
XV | 36 |
XVI | 40 |
XVII | 42 |
XVIII | 43 |
XIX | 49 |
XX | 57 |
XXII | 61 |
XXIII | 63 |
XXIV | 71 |
XXV | 74 |
XXVI | 77 |
XXVII | 80 |
XXVIII | 81 |
XXIX | 83 |
XXX | 85 |
XXXI | 91 |
XXXII | 93 |
XXXIII | 95 |
XXXV | 98 |
XXXVI | 100 |
XXXVII | 102 |
XXXIX | 103 |
XL | 107 |
XLI | 110 |
XLII | 117 |
XLIV | 118 |
XLV | 119 |
XLVII | 122 |
XLVIII | 123 |
XLIX | 131 |
L | 134 |
LI | 135 |
LII | 137 |
LIII | 139 |
LV | 143 |
LVI | 147 |
LVII | 149 |
LVIII | 155 |
LIX | 167 |
LX | 169 |
LXI | 170 |
LXII | 171 |
LXIII | 178 |
LXIV | 180 |
LXV | 182 |
LXVI | 186 |
LXVII | 189 |
LXVIII | 195 |
LXIX | 203 |
LXX | 204 |
LXXI | 209 |
LXXII | 213 |
LXXIII | 215 |
LXXXII | 258 |
LXXXIII | 261 |
LXXXIV | 263 |
LXXXV | 267 |
LXXXVI | 268 |
LXXXVII | 270 |
LXXXVIII | 274 |
LXXXIX | 278 |
XC | 282 |
XCI | 293 |
XCII | 294 |
XCIII | 295 |
XCIV | 297 |
XCVI | 301 |
XCVII | 302 |
XCVIII | 307 |
C | 309 |
CI | 311 |
CII | 312 |
CIII | 314 |
CIV | 321 |
CV | 333 |
CVI | 339 |
CVII | 344 |
CVIII | 353 |
CIX | 356 |
CX | 360 |
CXII | 363 |
CXIII | 366 |
CXIV | 367 |
CXV | 369 |
CXVII | 371 |
CXVIII | 374 |
CXIX | 377 |
CXX | 379 |
CXXII | 380 |
CXXIII | 382 |
CXXIV | 386 |
CXXVI | 387 |
CXXVII | 388 |
CXXVIII | 390 |
CXXIX | 392 |
CXXX | 398 |
CXXXI | 400 |
CXXXII | 402 |
CXXXIII | 407 |
CXXXIV | 409 |
CXXXV | 412 |
CXXXVI | 416 |
CXXXVIII | 419 |
CXXXIX | 420 |
CXL | 425 |
CXLI | 428 |
CXLII | 429 |
| 443 | |
| 445 | |
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Common terms and phrases
a a field a-field assume Borel-Cantelli Lemma bounded called Cauchy central limit theorem conditional expectation constant contingent claim convergence in distribution convergence in probability convergence theorem converges a.s. converges almost surely Corollary countable Define definition density disjoint distribution F distribution function dominated convergence Dominated Convergence Theorem equivalent example exists f XdP finite Fubini's theorem hence Hint iid random variables iid with common implies independent random variables index set inequality interval Kolmogorov large numbers Lebesgue measure Lemma lim inf lim sup martingale means monotone convergence non-decreasing non-negative Note positive martingale positive supermartingale probability measure probability space Proof Proposition prove Radon-Nikodym theorem random element random vari RECT regular result sample self-financing sequence of random Show stopping submartingale supermartingale Suppose X„,n sure convergence uniform integrability uniformly verify X\dP Zero-One Law
Bibliographic information
| Title | A Probability Path Modern Birkhäuser Classics, ISSN 2197-1803 |
| Author | Sidney Resnick |
| Edition | illustrated, reprint |
| Publisher | Springer Science & Business Media, 2003 |
| ISBN | 081764055X, 9780817640552 |
| Length | 453 pages |
| Subjects | › › Business & Economics / Operations Research Mathematics / Applied Mathematics / Probability & Statistics / General Mathematics / Probability & Statistics / Stochastic Processes |
| Export Citation | BiBTeX EndNote RefMan |