A User's Guide to Measure Theoretic Probability

Cover
Cambridge University Press, 2002 - 351 Seiten
This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
 

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Inhalt

II
1
V
3
VI
5
VII
7
VIII
11
IX
13
X
14
XI
17
LXXXIII
203
LXXXIV
205
LXXXV
206
LXXXVI
208
LXXXVII
211
XC
213
XCI
215
XCII
217

XIV
22
XV
26
XVI
29
XVII
31
XVIII
33
XIX
36
XX
37
XXI
39
XXII
41
XXIII
43
XXIV
45
XXV
51
XXVI
53
XXIX
58
XXX
59
XXXI
65
XXXII
68
XXXIII
70
XXXIV
71
XXXV
75
XXXVI
77
XXXVII
80
XXXVIII
83
XXXIX
88
XL
93
XLI
95
XLII
97
XLIII
99
XLIV
102
XLV
108
XLVI
111
XLVII
113
XLVIII
116
XLIX
118
L
121
LI
123
LII
128
LIII
131
LIV
135
LV
138
LVIII
142
LIX
147
LX
151
LXI
152
LXII
153
LXIII
155
LXIV
159
LXV
162
LXVI
166
LXVII
169
LXX
176
LXXI
182
LXXII
184
LXXIII
186
LXXIV
190
LXXV
193
LXXVIII
195
LXXIX
198
LXXXI
200
LXXXII
202
XCIII
219
XCIV
222
XCV
226
XCVI
228
XCVII
230
XCVIII
234
XCIX
237
C
239
CI
242
CII
244
CIII
248
CIV
249
CV
256
CVI
258
CVII
261
CVIII
264
CIX
266
CX
268
CXI
271
CXII
272
CXIII
274
CXVI
275
CXVII
276
CXVIII
278
CXIX
280
CXX
285
CXXI
287
CXXII
289
CXXIII
291
CXXIV
292
CXXV
294
CXXVI
295
CXXVII
296
CXXVIII
300
CXXX
301
CXXXI
302
CXXXII
303
CXXXIII
305
CXXXIV
306
CXXXVI
307
CXXXVII
308
CXXXVIII
310
CXXXIX
312
CXL
313
CXLI
315
CXLII
316
CXLIII
317
CXLVI
320
CXLVII
324
CXLVIII
329
CLI
332
CLII
334
CLIII
336
CLIV
338
CLVI
339
CLIX
342
CLX
343
CLXI
345
CLXII
347
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