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Zbl 0968.60071
Isozaki, Y.; Kotani, S.
Asymptotic estimates for the first hitting time of fluctuating additive functionals of Brownian motion. (English)
[A] Azéma, J. (ed.) et al., Séminaire de Probabilités XXXIV. Berlin: Springer. Lect. Notes Math. 1729, 374-387 (2000). ISBN 3-540-67314-8

A two-dimensional diffusion process $(X(t), Y(t))$ of a particular form with initial value $(x,y)$ is introduced. The authors investigate the asymptotic behavior of an exponential function of the first hitting time of the positive $y$-axis $T$. Applying this result, they estimate the probability of $\max_{0 \le s \le t} X(s) < |C|$ as $|C|^{\nu\rho} t^{-\rho/2}$ tends to $0$ for the case where the initial value $(x,y)$ equals $(0,0)$ and the constants $\nu, \rho$ lie in the interval $(0,1)$.
[Ching-Tang Wu (Wien)]

MSC 2000:: *60J65 Brownian motion

Keywords: first hitting time; asymptotic estimate

Cited in: Zbl 1145.60044

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