Geodesic
On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Weronika Łaukajtys1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toru/n, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 445-455

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/ba52-4-11
Keywords: convex set mathbb lipschitz operator defined space adapted processes adapted process semimartingale there exists unique strong solution following stochastic differential equation sde reflection boundary t int langle s rangle quad mathbb proofs based priori estimates solutions deterministic skorokhod problem

Weronika Łaukajtys 1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toru/n, Poland 
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Weronika Łaukajtys. On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) no. 4, pp. 445-455. doi: 10.4064/ba52-4-11

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