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 |
CVIII | 339 |
CIX | 344 |
CX | 353 |
CXI | 356 |
CXII | 360 |
CXIV | 363 |
CXV | 366 |
CXVI | 367 |
CXVII | 369 |
CXIX | 371 |
CXX | 374 |
CXXI | 377 |
CXXII | 379 |
CXXIV | 380 |
CXXV | 382 |
CXXVI | 386 |
CXXVIII | 387 |
CXXIX | 388 |
CXXX | 390 |
CXXXI | 392 |
CXXXII | 398 |
CXXXIII | 400 |
CXXXIV | 402 |
CXXXV | 407 |
CXXXVI | 409 |
CXXXVII | 412 |
CXXXVIII | 416 |
CXL | 419 |
CXLI | 420 |
CXLII | 425 |
CXLIII | 428 |
CXLIV | 429 |
| 443 | |
| 445 | |
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Common terms and phrases
B₁ B₂ Borel bounded Cauchy central limit theorem conditional expectation 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 E(Xn equivalent example exists finite fn(x Fubini's theorem hence Hint implies independent random variables index set inequality inf{n integrable interval Kolmogorov Lebesgue measure Lemma Let Xn lim inf lim sup martingale monotone convergence non-decreasing non-negative Note o-field P(An P(lim P[Xn P₁ positive supermartingale probability measure probability space Proof Proposition prove Radon-Nikodym theorem RECT regular result self-financing sequence of random Show stopping submartingale subsets supermartingale Suppose Xn sure convergence uniform integrability uniformly v₁ Var(X verify X₁ Xn+1 Xv^n Y₁