Abstract
This paper deals with an anticipating one-dimensional quasilinear stochastic differential equation of the Skorohod type. Some regularity properties of the solution are proved and we characterize the support of the law of the solution
Partially done when the author was visiting the “Centre de Recerca Matemàtica” at Barcelona.
Partially supported with the grant DGICYT PB90-0452.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aida, S., Kusuoka, S. and Stroock, D., ‘Òn the support of Wiener functionals”, Preprint, 1991.
Buckdahn, R., Quasilinear partial differential equations without nonanticipation requirement, Sektion Mathematik der Humboldt-Universität, Preprint 176. Berlin 1988.
Doss, H., Lien entre les équations différentielles stochastiques et ordinaires, Annales Inst. H. Poincaré, Sect. B. 13, 99–125 (1977).
Dunford, N. and Schwartz, J., Linear operators, Part I, Interscience Publishers Inc., 1957.
Ikeda, N. and Watanabe, S., Stochastic differential equations and diffusion processes, North Holland, New York, 1981.
Millet, A. and Nualart, D., Support theorems for a class of anticipating stochastic differential equations, Stochastic and Stochastics Reports 39, 1–24 (1992).
Millet, A., Nualart, D. and Sanz, M., Small perturbations for quasilinear anticipating stochastic differential equations, International series of Numerical Mathematics, Vol. 102, 149–157. Birkhaüser Verlag, Basel 1991.
Nguyen, M.D., Nualart, D. and Sanz, M., Application of Malliavin Calculus to a class of Stochastic Differential Equations, Probab. Th. Rel. Fields 84, 549–571 (1990).
Nualart, D. and Zakai, M., Multiple Wiener-Itô integrals possessing a continuous extension, Prob. Th. Rel. Fields, 85, 131–145 (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Basel AG
About this chapter
Cite this chapter
Millet, A., Sanz-Solé, M. (1993). On the Support of a Skorohod Anticipating Stochastic Differential Equation. In: Nualart, D., Solé, M.S. (eds) Barcelona Seminar on Stochastic Analysis. Progress in Probability, vol 32. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8555-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8555-3_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9677-1
Online ISBN: 978-3-0348-8555-3
eBook Packages: Springer Book Archive