Martingale-Valued Measures, Ornstein-Uhlenbeck Processes with Jumps and Operator Self-Decomposability in Hilbert Space
作者： David Applebaum
DOI: 10.1007/978-3-540-35513-7_14
关键词: Discrete mathematics 、 Ornstein–Uhlenbeck process 、 Pure mathematics 、 Martingale (probability theory) 、 Mathematics 、 Unitary operator 、 Weak operator topology 、 Multiplication operator 、 Projection-valued measure 、 Covariance operator 、 Trace class
摘要: We investigate a class of Hilbert space valued martingale-valued measures whose covariance structure is determined by trace positive operator measure. The paradigm example the martingale part Levy process. develop both weak and strong stochastic integration with respect to such measures. As an application, we convolution C0-semigroup process associated Ornstein-Uhlenbeck give in¯nite dimensional generalisation concept self-decomposability conditions for random variables this type be embedded into stationary
springer.com
springerlink.com参考文章(32)
Ken-iti Sato, Makoto Yamazato, Stationary processes of ornstein-uhlenbeck type Lecture Notes in Mathematics. ,vol. 1021, pp. 541- 551 ,(1983) , 10.1007/BFB0072949
R. Jajte, On stable distributions in Hilbert space Studia Mathematica. ,vol. 30, pp. 63- 71 ,(1968) , 10.4064/SM-30-1-63-71
Giuseppe Da Prato, Jerzy Zabczyk, Stochastic Equations in Infinite Dimensions ,(1992)
Werner Linde, Probability in Banach Spaces: Stable and Infinitely Divisible Distributions ,(1986)
David Applebaum, Lévy Processes and Stochastic Calculus ,(2004)
Hiroshi Kunita, Stochastic Integrals Based on Martingales Taking Values in Hilbert Space Nagoya Mathematical Journal. ,vol. 38, pp. 41- 52 ,(1970) , 10.1017/S0027763000013507
Frank Proske, Bernt Øksendal, Arne Løkka, Stochastic partial differential equations driven by Lévy space-time white noise Annals of Applied Probability. ,vol. 14, pp. 1506- 1528 ,(2004) , 10.1214/105051604000000413
Zbigniew J Jurek, Limit distributions and one-parameter groups of linear operators on Banach spaces Journal of Multivariate Analysis. ,vol. 13, pp. 578- 604 ,(1983) , 10.1016/0047-259X(83)90042-8
René Carmona, Harry Kesten, John B Walsh, John B Walsh, An introduction to stochastic partial differential equations Lecture Notes in Mathematics. pp. 265- 439 ,(1986) , 10.1007/BFB0074920
Zbigniew J. Jurek, J. David Mason, Operator-limit distributions in probability theory ,(1993)