On stochastic differential equations with reflecting boundary condition in convex domains

• Autorzy: Łaukajtys W.
• Języki publikacji: EN

Abstrakty

EN

Let D be an open convex set in R^d and let F be a Lipschitz operator defined on the space of adapted cadlag 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: Xt=Ht + integral of (F(X)s-, dZs] on the interval [0, t]+Kt, t belongs to R+. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

Słowa kluczowe

EN

stochastic differential equation with reflecting boundary; Skorokhod problem

PL

równanie różniczkowe stochastyczne; zagadnienie Skorochoda

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 4
• Strony: 445--455
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Łaukajtys W.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

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• [6] -, Stochastic Integration and Differential Equations, Springer, Berlin, 1990.
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• [10] A. Storm, Stochastic differential equations with a convex constraint, ibid. 53 (1995), 241-274.
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