The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains
| dc.contributor.author | Burdzy, Krzysztof | |
| dc.contributor.author | Chen, Zhen-Qing | |
| dc.contributor.author | Sylvester, John | |
| dc.date.accessioned | 2005-10-14T23:06:02Z | |
| dc.date.available | 2005-10-14T23:06:02Z | |
| dc.date.issued | 2004-01 | |
| dc.description.abstract | The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C3-smooth time-dependent domains in the n-dimensional Euclidean space Rn. Various sample path properties of RBM, its two-sided transition density functions estimate and the probabilistic representation of solutions for the corresponding partial differential equations are obtained. Furthermore, the onedimensional case is throughly studied, with the assumptions on the smoothness of the boundary drastically relaxed. | en |
| dc.description.sponsorship | National Science Foundation (NSF), National Security Agency (NSA), Office of Naval Research (ONR) | en |
| dc.format.extent | 238712 bytes | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.citation | The Annals of Probability 32, 775-804 | en |
| dc.identifier.uri | http://hdl.handle.net/1773/2131 | |
| dc.language.iso | en_US | |
| dc.publisher | Institute of Mathematical Statistics | en |
| dc.subject | Reflecting Brownian motion | en |
| dc.subject | Time-dependent domain | en |
| dc.subject | Local time | en |
| dc.subject | Skorohod decomposition | en |
| dc.subject | Heat equation with boundary conditions | en |
| dc.subject | Time-inhomogeneous strong Markov process | en |
| dc.subject | Probabilistic representation | en |
| dc.subject | Time-reversal | en |
| dc.subject | Feynman-Kac formula | en |
| dc.subject | Girsanov transform | en |
| dc.title | The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains | en |
| dc.type | Article | en |