| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Probability
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| Title: |
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Existence and asymptotic behaviour of some time-inhomogeneous diffusions |
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| Author(s): |
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Mihai Gradinaru ( ) 1, Yoann Offret ( ,  ) 1 |
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| Laboratory: |
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| Research team: |
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Processus stochastiques |
| Abstract: |
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Let us consider a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)|x|^\alpha/t^\beta$. This process can be viewed as a distorted Brownian motion in a potential, possibly singular, depending on time. After obtaining results on existence and 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 and explosion are proved for such processes. |
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| Fulltext language: |
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English |
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| Production date: |
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2009-11-18 |
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| Keyword(s): |
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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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| Classification: |
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60J60, 60H10, 60J65, 60G17, 60F15, 60F05 |
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| Comment: |
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29 pages |
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