On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains

Volume 52 / 2004

Weronika Łaukajtys Bulletin Polish Acad. Sci. Math. 52 (2004), 445-455 MSC: Primary 60H20. DOI: 10.4064/ba52-4-11

Abstract

Let $D$ be an open convex set in $\mathbb R^d$ and let $F$ be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process $H$ and any semimartingale $Z$ there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of $D$: $$ X_t=H_t+\int_0^t\, \langle F(X)_{s-},dZ_s\rangle + K_t, \ \quad t \in \mathbb R^+. $$ Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

Authors

  • Weronika ŁaukajtysFaculty of Mathematics and Computer Science
    Nicolaus Copernicus University
    Chopina 12/18
    87-100 Toru/n, Poland
    e-mail

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