Abstract
In this paper we introduce a notion of composition of skeletons for Wiener functionals and, as an application, we characterize the topological support of the law of the solution to a stochastic differential equation with random initial condition.
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
J.M. Bismut, Mécanique Aléatoire. Lecture Notes in Mathematics 866, Springer Verlag, 1981.
I. Gyöngy, On the support of the solutions of stochastic differential equations. Theory Probab. Appl. (1989), 649–653.
I. Gyöngy, D. Nualart and M. Sanz-Solé, Approximation and support theorems in modulus spaces, Probab. Theory Rel. Fields 101 (1995), 495–509.
V. Mackevičius, On the support of the solution of stochastic differential equations, Lietuvos Matmatikos Rinkinys XXXVI (1) (1986), 91–98.
A. Millet and D. Nualart, Support theorems for a class of anticipating stochastic differential equations. Stochastics and Stochastics Reports 39 (1992), 1–24.
A. Millet and M. Sanz-Solé. On the support of a Skorohod anticipating stochastic differential equation, in: Proceedings of the Barcelona Seminar on Stochastic Analysis, Progress in Probability 32 (1993), 103–131.
A. Millet and M. Sanz-Solé, A simple proof of the support theorem for diffusion processes, in: Seminaire de Probabilités XXVIII,Lecture Notes in Math. 1583 (1994), 36–48.
D. Stroock and S. R. S. Varadhan, On the support of diffusion processes with applications to the strong maximum principle. Proceedings of the Sixth Berkeley Symp. on Mathematical Statistics and Probability,Vol. III, (1972), 333–360.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this paper
Cite this paper
Caballero, M.E., Fernández, B., Nualart, D. (1997). Composition of Skeletons and Support Theorems. In: Stochastic Differential and Difference Equations. Progress in Systems and Control Theory, vol 23. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1980-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1980-4_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7365-3
Online ISBN: 978-1-4612-1980-4
eBook Packages: Springer Book Archive