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

Front Cover
Cambridge University Press, Sep 7, 2000 - Mathematics - 496 pages
2 Reviews
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
LXXXIV
239
LXXXV
246
LXXXVI
250
LXXXVII
263
LXXXVIII
265
LXXXIX
266
XC
267
XCI
269

XII
15
XIII
16
XIV
17
XV
18
XVI
20
XVII
21
XVIII
23
XIX
24
XX
25
XXI
27
XXII
29
XXIII
30
XXIV
33
XXV
37
XXVI
42
XXVII
45
XXVIII
46
XXIX
47
XXX
50
XXXI
52
XXXII
57
XXXIII
58
XXXIV
63
XXXV
64
XXXVI
69
XXXVII
73
XXXVIII
75
XXXIX
79
XL
83
XLI
86
XLII
89
XLIII
93
XLIV
95
XLV
99
XLVI
102
XLVII
106
XLVIII
108
XLIX
110
L
112
LI
113
LII
114
LIV
117
LV
119
LVI
122
LVII
124
LVIII
125
LIX
128
LX
132
LXI
136
LXII
141
LXIII
144
LXIV
149
LXV
151
LXVI
155
LXVII
158
LXVIII
160
LXIX
162
LXX
163
LXXI
166
LXXII
170
LXXIII
173
LXXIV
175
LXXV
177
LXXVI
178
LXXVII
181
LXXVIII
182
LXXIX
186
LXXX
193
LXXXI
198
LXXXII
203
LXXXIII
224
XCII
270
XCIII
271
XCIV
273
XCV
276
XCVI
284
XCVII
289
XCVIII
291
XCIX
295
C
297
CI
300
CII
301
CIII
304
CIV
308
CV
313
CVI
315
CVII
317
CVIII
318
CIX
319
CX
322
CXI
327
CXII
329
CXIII
331
CXIV
332
CXV
334
CXVI
336
CXVII
338
CXVIII
340
CXIX
343
CXX
346
CXXI
347
CXXII
349
CXXIII
350
CXXIV
352
CXXV
354
CXXVI
358
CXXVII
359
CXXVIII
360
CXXIX
361
CXXX
364
CXXXI
367
CXXXII
369
CXXXIII
372
CXXXIV
374
CXXXV
375
CXXXVI
376
CXXXVII
377
CXXXVIII
382
CXXXIX
388
CXL
391
CXLI
394
CXLIII
398
CXLIV
400
CXLV
405
CXLVI
406
CXLVII
410
CXLVIII
413
CXLIX
416
CL
418
CLI
420
CLII
425
CLIII
428
CLIV
431
CLV
432
CLVI
433
CLVII
438
CLVIII
439
CLIX
442
CLX
445
CLXI
449
CLXII
469
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About the author (2000)

Dr. Williams currently leads the Oral Microbiology Group based at the School of Dentistry, at Cardiff University, Cardiff, UK. Since Dr. Williams' first degree (Cardiff University), he has worked in the pharmaceutical industry, food microbiology and as an academic researcher. Having completed a PhD at the School of Dentistry in Cardiff on the immunopathogenesis of oral candidosis, Dr. Williams' research has continued within Cardiff University and primarily focuses within the field of Clinical Microbiology with an emphasis on studies involving microbial biofilms. Dr. Williams' research encompasses investigating biofilm susceptibility to antimicrobial agents, expression of virulence factors such as hydrolytic enzyme production, adhesion, and microbial modulation of innate immune responses. Of particular interest has been research into the development of biomaterials (e.g. silicone rubber, acrylic, titanium) to inhibit biofilm formation on medical devices. Dr. Williams is a previous recipient of the Senior Colgate Award (British Society for Oral and Dental Research) and the International Hatton Award (The International Association for Dental Research).

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