On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Weronika Łaukajtys
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004), p. 445-455 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let D be an open convex set in ℝd 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: Xt=Ht+∫0t⟨F(X)s-,dZs⟩+Kt, t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:280926 
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-11,
     author = {Weronika \L aukajtys},
     title = {On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {52},
     year = {2004},
     pages = {445-455},
     zbl = {1138.60327},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-11}
}

Weronika Łaukajtys. On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 52 (2004) pp. 445-455. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba52-4-11/