Skorohod stochastic differential equations with boundary conditions
- 1 December 1993
- journal article
- research article
- Published by Taylor & Francis in Stochastics and Stochastic Reports
- Vol. 45 (3) , 211-235
- https://doi.org/10.1080/17442509308833862
Abstract
In this paper we prove the existence and uniqueness of a solution for a one-dimensional quasilinear stochastic differential equation of the Skorohod type, with a non-linear boundary condition of the form . The method of proof uses the Girsanov transformation and some basic exponential estimates. When the coefficients of the equation are deterministic we show that the solution is weakly differentiable on the Wiener space and possesses a continuous modification.Keywords
This publication has 6 references indexed in Scilit:
- Skorohod stochastic differential equations of diffusion typeProbability Theory and Related Fields, 1992
- Boundary Value Problems for Stochastic Differential EquationsThe Annals of Probability, 1991
- Applications of anticipating stochastic calculus to stochastic differential equationsPublished by Springer Nature ,1990
- Linear stochastic differential equations with boundary conditionsProbability Theory and Related Fields, 1989
- Stochastic calculus with anticipating integrandsProbability Theory and Related Fields, 1988
- Generalized stochastic integrals and the malliavin calculusProbability Theory and Related Fields, 1986