Abstract
We define an anticipative stochastic integral of Stratonovich type with respect to a nonhomogeneous Wiener process in the dual of a nuclear space and investigate its basic properties.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Bojdecki T, Jakubowski J (1989) Ito stochastic integral in the dual of a nuclear space. J Multivariate Anal 31:40–58
Bojdecki T, Jakubowski J (1990) Stochastic integration for inhomogenous Wiener process in the dual of a nuclear space. J Multivariate Anal 34:185–210
Bojdecki T, Jakubowski J (1993) The Skorohod integral in conuclear spaces. Appl Math Optim 28:87–110
Gorostiza LG (1983) High density limit theorems for infinite systems of unscaled branching Brownian motions. Ann Probab 11:374–392
Grorud A, Pardoux E (1991) Intégrales Hilbertiennes anticipantes par rapport à un processus de Wiener cylindrique et calcul stochastique associé. Appl Math Optim 25:31–49
Hitsuda M, Mitoma I (1986) Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions. J Multivariate Anal 19:311–328
Kallianpur G, Pérez-Abreu V (1991) The Skorohod integral and the derivative operator of functionals of a cylindrical Brownian motion. Appl Math Optim 25:11–29
Kallianpur G, Wolpert RL (1984) Infinite-dimensional stochastic differential equation models for spacially distributed neurons. Appl Math Optim 12:125–172
Nualart D, Pardoux E (1988) Stochastic calculus with anticipating integrands. Probab Theory Related Fields 78:535–581
Pérez-Abreu V (1992) Anticipating solutions of stochastic bilinear equations in Hilbert spaces. LG Gorostiza, J Léon (editors) Contribuciones en Probabilidad y Estadística Matemática 3, Proceedings IV CLAPEM, México, pp 297–312
Walsh JB (1986) An introduction to Stochastic Partial Differential Equations. Lecture Notes in Mathematics, vol 1180. Springer-Verlag, Berlin, pp 266–439
Author information
Authors and Affiliations
Additional information
This research was partially supported by Komitet Badań Naukowych, Grant 2 1094 91 01.
Rights and permissions
About this article
Cite this article
Bojdecki, T., Jakubowski, J. The anticipative Stratonovich integral in conuclear spaces. Appl Math Optim 34, 91–111 (1996). https://doi.org/10.1007/BF01182475
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01182475