Semimartingales: A Course on Stochastic ProcessesWalter 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 |
273 | |
286 | |
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Expressions et termes fréquents
adapted admissible measure assume B-valued Banach space Borel Brownian motion chapter condition consider continuous converges a. s. Corollary decomposition defined definition denote denumerable Doleans dual predictable projection E(sup equation exists F-measurable F₁ filtration finite variation following property follows immediately formula function H₁ Hilbert space implies increasing sequence inequality integral with respect jumps Lemma linear local martingale M₁ mapping Markov process Math o-additive o-algebra orthogonal P-equality paths point process Poisson process predictable process predictable stopping Proof Proposition prove quasimartingale R. R. C. process random measure random variable real process resp right-continuous semimartingale sequence of stopping shows square integrable square integrable martingale stochastic basis stochastic integral strong solution submartingale subset supermartingale T₁ Theorem totally inaccessible uniformly integrable unique usual hypotheses write X₁
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