Existence and asymptotic behaviour of some time-inhomogeneous diffusions. (English. French summary) Zbl 1267.60091

A scalar diffusion with a time-dependent drift of the form \(\rho \operatorname{sgn}(x)|x|^{\alpha}/t^{\beta}\) that is the subgradient of a certain potential, is analyzed for various values of the parameters \(\rho, \alpha, \beta\) and the initial data. The results include existence and uniqueness of path-wise or weak solutions, conditions for explosion and non-explosion, transience and recurrence in a suitable sense, and limit theorems, both distributional and almost sure ones, for suitable scalings.


60J60 Diffusion processes
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J25 Continuous-time Markov processes on general state spaces
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