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 |
LXXVIII | 219 |
LXXIX | 222 |
LXXX | 226 |
LXXXI | 230 |
LXXXII | 234 |
LXXXIII | 247 |
LXXXIV | 252 |
LXXXV | 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 |
XXVII | 74 |
XXVIII | 77 |
XXIX | 80 |
XXX | 81 |
XXXI | 83 |
XXXII | 85 |
XXXIII | 91 |
XXXIV | 93 |
XXXV | 95 |
XXXVII | 98 |
XXXVIII | 100 |
XXXIX | 102 |
XLI | 103 |
XLII | 107 |
XLIII | 110 |
XLIV | 117 |
XLVI | 118 |
XLVII | 119 |
XLIX | 122 |
L | 123 |
LI | 131 |
LII | 134 |
LIII | 135 |
LIV | 137 |
LV | 139 |
LVII | 143 |
LVIII | 147 |
LIX | 149 |
LX | 155 |
LXI | 167 |
LXII | 169 |
LXIII | 170 |
LXIV | 171 |
LXV | 178 |
LXVI | 180 |
LXVII | 182 |
LXVIII | 186 |
LXIX | 189 |
LXX | 195 |
LXXI | 203 |
LXXIV | 204 |
LXXV | 209 |
LXXVI | 213 |
LXXVII | 215 |
LXXXVI | 258 |
LXXXVII | 261 |
LXXXVIII | 263 |
LXXXIX | 267 |
XC | 268 |
XCI | 270 |
XCII | 274 |
XCIII | 278 |
XCIV | 282 |
XCV | 293 |
XCVI | 294 |
XCVII | 295 |
XCVIII | 297 |
C | 301 |
CI | 302 |
CII | 307 |
CIV | 309 |
CV | 311 |
CVI | 312 |
CVII | 314 |
CVIII | 321 |
CIX | 333 |
CX | 339 |
CXI | 344 |
CXII | 353 |
CXIII | 356 |
CXIV | 360 |
CXVI | 363 |
CXVII | 366 |
CXVIII | 367 |
CXIX | 369 |
CXXI | 371 |
CXXII | 374 |
CXXIII | 377 |
CXXIV | 379 |
CXXVI | 380 |
CXXVII | 382 |
CXXVIII | 386 |
CXXX | 387 |
CXXXI | 388 |
CXXXII | 390 |
CXXXIII | 392 |
CXXXIV | 398 |
CXXXV | 400 |
CXXXVI | 402 |
CXXXVII | 407 |
CXXXVIII | 409 |
CXXXIX | 412 |
CXL | 416 |
CXLII | 419 |
CXLIII | 420 |
CXLIV | 425 |
CXLV | 428 |
CXLVI | 429 |
| 443 | |
| 445 | |
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Common terms and phrases
B₁ Borel bounded Cauchy central limit theorem conditional expectation continuous convergence in distribution convergence in probability convergence theorem converges a.s. converges almost surely Corollary countable Define definition density disjoint distribution function dominated convergence equivalent example exists finite fn(x Fubini's theorem hence Hint implies independent random variables index set inequality inf{n integrable interval Kolmogorov L₁ Lebesgue measure Lemma Let Xn lim inf lim sup limn martingale monotone convergence n-system non-decreasing non-negative Note o-additive o-field P(An P(lim P[Xn probability measure probability space Proof Proposition prove result S₁ self-financing sequence of random Show Xn submartingale subsets supermartingale Suppose Xn sure convergence uniform integrability uniformly v₁ Var(X verify X\dP X₁ Xn+1 Βη μη ξη Ση Χη