# Existence and asymptotic behaviour of some time-inhomogeneous diffusions

Annales de l'I.H.P. Probabilités et statistiques (2013)

- Volume: 49, Issue: 1, page 182-207
- ISSN: 0246-0203

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topGradinaru, Mihai, and Offret, Yoann. "Existence and asymptotic behaviour of some time-inhomogeneous diffusions." Annales de l'I.H.P. Probabilités et statistiques 49.1 (2013): 182-207. <http://eudml.org/doc/271961>.

@article{Gradinaru2013,

abstract = {Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient $\rho \operatorname\{sgn\}(x)|x|^\{\alpha \}/t^\{\beta \}$. This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, 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 and explosion are proved for such processes.},

author = {Gradinaru, Mihai, Offret, Yoann},

journal = {Annales de l'I.H.P. Probabilités et statistiques},

keywords = {time-inhomogeneous diffusions; time dependent potential; singular stochastic differential equations; explosion times; scaling transformations; change of time; recurrence and transience; iterated logarithm type laws; asymptotic distributions; scalar diffusion; time-dependent drift; transience; recurrence; asymptotic behavior},

language = {eng},

number = {1},

pages = {182-207},

publisher = {Gauthier-Villars},

title = {Existence and asymptotic behaviour of some time-inhomogeneous diffusions},

url = {http://eudml.org/doc/271961},

volume = {49},

year = {2013},

}

TY - JOUR

AU - Gradinaru, Mihai

AU - Offret, Yoann

TI - Existence and asymptotic behaviour of some time-inhomogeneous diffusions

JO - Annales de l'I.H.P. Probabilités et statistiques

PY - 2013

PB - Gauthier-Villars

VL - 49

IS - 1

SP - 182

EP - 207

AB - Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient $\rho \operatorname{sgn}(x)|x|^{\alpha }/t^{\beta }$. This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, 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 and explosion are proved for such processes.

LA - eng

KW - time-inhomogeneous diffusions; time dependent potential; singular stochastic differential equations; explosion times; scaling transformations; change of time; recurrence and transience; iterated logarithm type laws; asymptotic distributions; scalar diffusion; time-dependent drift; transience; recurrence; asymptotic behavior

UR - http://eudml.org/doc/271961

ER -

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