TY - JOUR
T1 - Spinning Brownian motion
AU - Duarte, Mauricio A.
N1 - Funding Information:
Most of the research leading to this publication was conducted during my graduate studies at the University of Washington. I would like to thank my advisor Krzysztof Burdzy for introducing me to the problem discussed in this article, and for many conversations that helped me to successfully conduct this research. During this time, my research was funded by the US National Science Foundation grant number DMS 090-6743 .
Funding Information:
The preparation of this manuscript was partially funded by FONDECYT , project no. 3130724 . We also acknowledge support of Programa Iniciativa Cientifica Milenio grant number NC130062 through the Nucleus Millenium Stochastic Models of Complex and Disordered Systems.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2015/11/1
Y1 - 2015/11/1
N2 - We prove strong existence and uniqueness for a reflection process X in a smooth, bounded domain D that behaves like obliquely-reflected-Brownian-motion, except that the direction of reflection depends on a (spin) parameter S, which only changes when X is on the boundary of D according to a physical rule. The process (X,S) is a degenerate diffusion. We show uniqueness of the stationary distribution by using techniques based on excursions of X from ∂D, and an associated exit system. We also show that the process admits a submartingale formulation and use related results to show examples of the stationary distribution.
AB - We prove strong existence and uniqueness for a reflection process X in a smooth, bounded domain D that behaves like obliquely-reflected-Brownian-motion, except that the direction of reflection depends on a (spin) parameter S, which only changes when X is on the boundary of D according to a physical rule. The process (X,S) is a degenerate diffusion. We show uniqueness of the stationary distribution by using techniques based on excursions of X from ∂D, and an associated exit system. We also show that the process admits a submartingale formulation and use related results to show examples of the stationary distribution.
KW - Degenerate reflected diffusion
KW - Excursion theory
KW - Stationary distribution
KW - Stochastic differential equations
UR - http://www.scopus.com/inward/record.url?scp=84939654192&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2015.06.005
DO - 10.1016/j.spa.2015.06.005
M3 - Article
AN - SCOPUS:84939654192
SN - 0304-4149
VL - 125
SP - 4178
EP - 4203
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 11
ER -