Diffusions, Markov Processes and Martingales: Volume 2, Itô Calculus

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Cambridge University Press, Sep 7, 2000 - Mathematics - 496 pages
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This celebrated book has been prepared with readers' needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
 

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Contents

II
1
III
2
V
4
VI
8
VII
9
VIII
10
IX
11
X
14
LXXXIX
239
XC
246
XCI
250
XCII
263
XCIV
264
XCV
264
XCVI
265
XCVII
267

XII
15
XIII
16
XIV
17
XV
18
XVI
20
XVII
21
XVIII
23
XIX
24
XX
25
XXI
27
XXII
29
XXIII
30
XXV
33
XXVI
37
XXVII
42
XXX
45
XXXI
46
XXXII
47
XXXIII
50
XXXIV
52
XXXVII
57
XXXVIII
58
XXXIX
63
XL
64
XLI
69
XLII
73
XLIII
75
XLIV
79
XLV
83
XLVI
86
XLVII
89
XLVIII
93
XLIX
95
L
99
LI
102
LII
106
LIII
108
LIV
110
LV
112
LVI
113
LVII
114
LIX
117
LX
119
LXI
122
LXII
124
LXIII
125
LXIV
128
LXV
132
LXVI
136
LXVII
141
LXVIII
144
LXIX
149
LXX
151
LXXI
155
LXXII
158
LXXIII
160
LXXIV
162
LXXV
163
LXXVI
166
LXXVII
170
LXXVIII
173
LXXIX
175
LXXX
177
LXXXI
178
LXXXII
181
LXXXIII
182
LXXXIV
186
LXXXV
193
LXXXVI
198
LXXXVII
203
LXXXVIII
224
XCVIII
268
C
269
CI
271
CII
274
CIII
282
CIV
287
CV
289
CVI
293
CVII
295
CVIII
298
CIX
299
CX
302
CXIV
306
CXV
311
CXVI
313
CXVII
315
CXVIII
316
CXIX
317
CXX
320
CXXI
325
CXXII
327
CXXIII
329
CXXIV
330
CXXVI
332
CXXVII
334
CXXVIII
336
CXXIX
338
CXXX
341
CXXXI
344
CXXXII
345
CXXXIV
347
CXXXV
348
CXXXVI
350
CXXXVII
352
CXXXVIII
356
CXXXIX
357
CXL
358
CXLI
359
CXLII
362
CXLIII
365
CXLV
367
CXLVI
370
CXLVII
372
CXLVIII
373
CXLIX
374
CL
375
CLI
380
CLIII
386
CLIV
389
CLV
392
CLVII
396
CLIX
398
CLX
403
CLXI
404
CLXII
408
CLXIII
411
CLXIV
414
CLXV
416
CLXVI
418
CLXVII
423
CLXVIII
426
CLXIX
429
CLXX
430
CLXXI
431
CLXXII
436
CLXXIII
437
CLXXIV
440
CLXXV
443
CLXXVI
447
CLXXVII
467
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