An approximation scheme for reflected stochastic differential equations
In this paper, we consider the Stratonovich reflected SDE in a bounded domain . Letting be the N-dyadic piecewise linear interpolation of Wt, we show that the distribution of the solution to the reflected ODE converges weakly to that of (Xt,Lt). Hence, we prove a distributional version for reflected diffusions of the famous result of Wong and Zakai. In particular, we apply our result to derive some geometric properties of coupled reflected Brownian motion, especially those properties which have been used in the recent work on the "hot spots" conjecture for special domains.
Year of publication: |
2011
|
---|---|
Authors: | Evans, Lawrence Christopher ; Stroock, Daniel W. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 7, p. 1464-1491
|
Publisher: |
Elsevier |
Keywords: | Wong-Zakai approximation Reflected stochastic differential equation |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
On the Derivation of the Black-Scholes Formula
Rosu, Ioanid, (2013)
-
Deuschel, Jean-Dominique, (1989)
- More ...