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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.

MSC:
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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