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• W3100823986 abstract "We consider a diffusion process X in a random Lévy potential $mathbb{V}$ which is a solution of the informal stochastic differential equation $$begin{eqnarray*}cases{dX_{t}=dbeta_{t}-frac{1}{2}mathbb{V}'(X_{t}),dt,cr X_{0}=0,}end{eqnarray*}$$ (β B. M. independent of $mathbb{V}$). We study the rate of convergence when the diffusion is transient under the assumption that the Lévy process $mathbb{V}$ does not possess positive jumps. We generalize the previous results of Hu–Shi–Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that there exists 0<κ<1 such that $mathbf{E}[e^{kappamathbb{V}_{1}}]=1$, then Xt/tκ converges to some nondegenerate distribution. These results are in a way analogous to those obtained by Kesten–Kozlov–Spitzer for the transient random walk in a random environment." @default.
• W3100823986 created "2020-11-23" @default.
• W3100823986 creator A5053875223 @default.
• W3100823986 date "2008-01-01" @default.
• W3100823986 modified "2023-10-16" @default.
• W3100823986 title "Rates of convergence of a transient diffusion in a spectrally negative Lévy potential" @default.
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• W3100823986 doi "https://doi.org/10.1214/009117907000000123" @default.
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