Semimartingales: A Course on Stochastic Processes

Couverture
Walter de Gruyter, 1982 - 287 pages
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
 

Table des matières

Basic notions on stochastic processes
3
The predictable F V process of an admissible measure on A and
15
Martingales and quasimartingales Basic inequalities and convergence
40
Doobs inequalities for real quasimartingales and the almost sure
46
Uniform integrability Convergence in LP Regularity properties
53
Convergence theorems for vectorvalued quasimartingales
61
Exercises and supplements
72
Historical and bibliographical notes
79
Localisation of processes and semimartingales
148
Stochastic integral with respect to semimartingales and
167
Quadratic variation and the transformation theorem
175
Stochastic integral with respect to multidimensional semimartingales
182
The transformation formula in the multidimensional case
188
First applications of the transformation theorem
198
Absolutely continuous changes of probablity
207
Random measures and local characteristics of a semimartingale
217

Doleans measure of an L D quasimartingale
87
Square integrable Martingales and semimartingales
111
The L2stochastic integral and the quadratic variation of an L2martingale
121
Stopped martingales Inequalities
128
The process M of a square integrable Hilbertvalued martingale
136
The isometric stochastic integral with respect to Hilbertvalued martingales
142
Local characteristics of a semimartingaleDiffusionsMartingale problems
231
Stochastic differential equations
239
Conditions for nonexplosion
252
Bibliography
273
Index
286
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

Fréquemment cités

Page 276 - Stabilité des solutions des équations différentielles stochastiques. Application aux intégrales multiplicatives stochastiques.
Page 275 - Existence du processus croissant naturel associé à un potentiel de classe (D). ' Z. Wahrscheinlichkeitstheorie verw.
Page 277 - J. PELLAUMAIL, Formule de Ito pour des processus à valeurs dans des espaces de Banach, Ann. Inst. Henri Poincarè, vol. X, no. 4 (1974), pp. 399-422. [9] BS KASIN, Mat. Zametki, 14 (1973), pp. 645-654. [10] W. MATUSZEWSKA and W. OBLICZ, A note on modular space

Informations bibliographiques