Langevin process reflected on a partially elastic boundary I
| Autor: | Emmanuel Jacob |
|---|---|
| Přispěvatelé: | Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Jacob, Emmanuel |
| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Statistics and Probability
Stationarity [MATH.MATH-PR] Mathematics [math]/Probability [math.PR] Second-order reflection Boundary (topology) Reflecting boundary 01 natural sciences 010104 statistics & probability Second order reflexion Modelling and Simulation FOS: Mathematics Renewal theory Uniqueness 0101 mathematics 10. No inequality ComputingMilieux_MISCELLANEOUS Brownian motion Mathematics Ladder height process Applied Mathematics 010102 general mathematics Mathematical analysis Probability (math.PR) Zero (complex analysis) Random walk Ladder height processes [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Reflection (mathematics) Modeling and Simulation Brownian dynamics Langevin process Mathematics - Probability |
| Zdroj: | Stochastic Processes and their Applications Stochastic Processes and their Applications, Elsevier, 2012, 122 (1), pp.191-216 Stochastic Processes and their Applications, 2012, 122 (1), pp.191-216. ⟨10.1016/j.spa.2011.08.003⟩ |
| ISSN: | 0304-4149 1879-209X |
| DOI: | 10.1016/j.spa.2011.08.003⟩ |
| Popis: | Consider a Langevin process, that is an integrated Brownian motion, constrained to stay on the nonnegative half-line by a partially elastic boundary at 0. If the elasticity coefficient of the boundary is greater than or equal to a critical value (0.16), bounces will not accumulate in a finite time when the process starts from the origin with strictly positive velocity. We will show that there exists then a unique entrance law from the boundary with zero velocity, despite the immediate accumulation of bounces. This result of uniqueness is in sharp contrast with the literature on deterministic second order reflection. Our approach uses certain properties of real-valued random walks and a notion of spatial stationarity which may be of independent interest. 30 pages, 1 figure. In this new version, the introduction and the preliminaries in particular have been rewritten (for a dramatic change) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect