Stochastic Integration With Jumps
, by Klaus BichtelerNote: Supplemental materials are not guaranteed with Rental or Used book purchases.
 ISBN: 9780521811293  0521811295
 Cover: Hardcover
 Copyright: 5/13/2002
Stochastic processes with jumps and random measures are importance as drivers in applications like financial mathematics and signal processing. This 2002 text develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs results from ordinary integration theory, for instance previsible envelopes and an algorithm computing stochastic integrals of cáglád integrands pathwise. Full proofs are given for all results, and motivation is stressed throughout. A large appendix contains most of the analysis that readers will need as a prerequisite. This will be an invaluable reference for graduate students and researchers in mathematics, physics, electrical engineering and finance who need to use stochastic differential equations.
Klaus Bichteler is a Professor of Mathematics at the University of Texas at Austin.
Preface  xi  

1  (42)  

1  (8)  

4  (1)  

5  (1)  

6  (3)  

9  (11)  

11  (3)  

14  (3)  

17  (1)  

18  (2)  

20  (23)  

21  (1)  

22  (1)  

23  (4)  

27  (2)  

29  (3)  

32  (1)  

33  (1)  

34  (2)  

36  (7)  

43  (44)  

43  (3)  

46  (7)  

46  (1)  

47  (1)  

47  (2)  

49  (2)  

51  (2)  

53  (5)  

54  (2)  

56  (1)  

56  (2)  

58  (9)  

58  (3)  

61  (1)  

62  (1)  

63  (1)  

64  (3)  

67  (4)  

69  (1)  

70  (1)  

71  (16)  

73  (1)  

74  (2)  

76  (1)  

77  (1)  

78  (2)  

80  (7)  

87  (100)  

87  (1)  

88  (6)  

89  (1)  

90  (4)  

94  (12)  

95  (2)  

97  (2)  

99  (2)  

101  (1)  

101  (1)  

102  (2)  

104  (2)  

106  (4)  

109  (1)  

110  (5)  

111  (1)  

112  (1)  

113  (1)  

114  (1)  

115  (8)  

115  (3)  

118  (1)  

118  (4)  

122  (1)  

123  (7)  

123  (1)  

124  (1)  

125  (3)  

128  (1)  

129  (1)  

130  (15)  

132  (3)  

135  (2)  

137  (1)  

138  (2)  

140  (4)  

144  (1)  

145  (12)  

148  (2)  

150  (3)  

153  (2)  

155  (2)  

157  (14)  

159  (2)  

161  (1)  

162  (6)  

168  (3)  

171  (16)  

174  (1)  

175  (2)  

177  (3)  

180  (3)  

183  (1)  

184  (1)  

185  (2)  

187  (84)  

187  (22)  

187  (4)  

191  (4)  

195  (10)  

205  (4)  

209  (12)  

209  (4)  

213  (3)  

216  (2)  

218  (1)  

219  (2)  

221  (11)  

222  (3)  

225  (2)  

227  (1)  

228  (3)  

231  (1)  

232  (6)  

233  (1)  

234  (4)  

238  (15)  

239  (7)  

246  (5)  

251  (2)  

253  (18)  

257  (4)  

261  (4)  

265  (2)  

267  (1)  

268  (3)  

271  (92)  

271  (11)  

272  (1)  

273  (5)  

278  (2)  

280  (2)  

282  (16)  

283  (2)  

285  (4)  

289  (4)  

293  (3)  

296  (1)  

297  (1)  

298  (12)  

301  (2)  

303  (2)  

305  (5)  

310  (20)  

311  (3)  

314  (2)  

316  (1)  

317  (3)  

320  (1)  

321  (5)  

326  (4)  

330  (13)  

332  (1)  

333  (4)  

337  (6)  

343  (8)  

343  (3)  

346  (1)  

347  (2)  

349  (2)  

351  (12)  

351  (12)  
Appendix A Complements to Topology and Measure Theory  363  (107)  

363  (3)  

366  (25)  

366  (7)  

373  (3)  

376  (1)  

377  (2)  

379  (3)  

382  (6)  

388  (3)  

391  (30)  

391  (1)  

391  (3)  

394  (4)  

398  (3)  

401  (1)  

402  (2)  

404  (1)  

405  (1)  

406  (1)  

407  (1)  

408  (1)  

409  (4)  

413  (1)  

414  (5)  

419  (2)  

421  (11)  

425  (1)  

426  (6)  

432  (8)  

436  (4)  

440  (1)  

440  (3)  

440  (3)  

443  (5)  

448  (15)  

453  (2)  

455  (3)  

458  (5)  

463  (7)  

463  (2)  

465  (2)  

467  (3)  
Appendix B Answers to Selected Problems  470  (7)  
References  477  (6)  
Index of Notations  483  (6)  
Index  489 