On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains

Weronika Łaukajtys

Bulletin of the Polish Academy of Sciences. Mathematics (2004)

  • Volume: 52, Issue: 4, page 445-455
  • ISSN: 0239-7269

Abstract

top
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 - , d Z s ⟩ + K t , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

How to cite

top

Weronika Łaukajtys. "On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains." Bulletin of the Polish Academy of Sciences. Mathematics 52.4 (2004): 445-455. <http://eudml.org/doc/280926>.

@article{WeronikaŁaukajtys2004,
abstract = {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.},
author = {Weronika Łaukajtys},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {stochastic differential equation with reflecting boundary; Skorokhod problem},
language = {eng},
number = {4},
pages = {445-455},
title = {On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains},
url = {http://eudml.org/doc/280926},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Weronika Łaukajtys
TI - On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 4
SP - 445
EP - 455
AB - 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.
LA - eng
KW - stochastic differential equation with reflecting boundary; Skorokhod problem
UR - http://eudml.org/doc/280926
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.