On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains

• Autorzy: Weronika Łaukajtys
• 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 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:
$X_t = H_t + ∫_0^t ⟨F(X)_{s-},dZ_s⟩ + K_t$, t ∈ ℝ⁺.
Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

Kategorie tematyczne

• 60H20: Stochastic integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: 52
• Numer: 4
• Strony: 445-455

Daty

wydano

2004

Twórcy

autor

Weronika Łaukajtys

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

Identyfikatory

DOI

10.4064/ba52-4-11