Spinning Brownian motion

Resultado de la investigación: Article

Resumen

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.

Idioma originalEnglish
Páginas (desde-hasta)4178-4203
Número de páginas26
PublicaciónStochastic Processes and their Applications
Volumen125
N.º11
DOI
EstadoPublished - 1 nov 2015

Huella dactilar

Brownian movement
Brownian motion
Stationary Distribution
Submartingale
Reflected Brownian Motion
Degenerate Diffusion
Excursion
Bounded Domain
Existence and Uniqueness
Uniqueness
Formulation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Citar esto

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abstract = "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.",
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Spinning Brownian motion. / Duarte, Mauricio A.

En: Stochastic Processes and their Applications, Vol. 125, N.º 11, 01.11.2015, p. 4178-4203.

Resultado de la investigación: Article

TY - JOUR

T1 - Spinning Brownian motion

AU - Duarte, Mauricio A.

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

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U2 - 10.1016/j.spa.2015.06.005

DO - 10.1016/j.spa.2015.06.005

M3 - Article

VL - 125

SP - 4178

EP - 4203

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

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