941 articles – 1212 references  [version française]
 HAL: hal-00433274, version 1
 arXiv: 0911.3534
 Available versions: v1 (2009-11-18) v2 (2010-09-23) v3 (2011-04-12) v4 (2012-04-23)
 Asymptotic behaviour of a family of time-inhomogeneous diffusions
 Mihai Gradinaru ( ) 1, Yoann Offret 1
 (2009-11-18)
 Let $X$ a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)\frac{|x|^\alpha}{t^\beta}$. This process can be viewed as a distorted Brownian motion in a potential possibly singular, depending on time. After obtaining results on the existence and the uniqueness of solution, we study its asymptotic behaviour and made a precise description, in terms of parameters $\rho,\alpha$ and $\beta$, of the recurrence, transience and convergence. More precisely, asymptotic distributions, iterated logarithm type laws and rates of transience are proved for such processes.
 1: Institut de Recherche Mathématique de Rennes (IRMAR) CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne
 Subject : Mathematics/Probability
 Keyword(s): time-inhomogeneous diffusions – singular stochastic differential equations – explosion times – scaling transformations and changes of time – recurrence and transience – iterated logarithm type laws – asymptotic distributions
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 hal-00433274, version 1 http://hal.archives-ouvertes.fr/hal-00433274 oai:hal.archives-ouvertes.fr:hal-00433274 From: Mihai Gradinaru <> Submitted on: Wednesday, 18 November 2009 16:12:36 Updated on: Wednesday, 18 November 2009 17:12:57