Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes

Bernard Roynette; Pierre Vallois; Agnès Volpi

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Long-term behavior for superprocesses over a stochastic flow.

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Brownian particles with electrostatic repulsion on the circle : Dyson’s model for unitary random matrices revisited

Emmanuel Cépa, Dominique Lépingle (2001)

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The brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices $N \times N$ is interpreted as a system of $N$ interacting brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles $N$ goes to infinity (through the empirical measure process). We prove that...

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The Cauchy problem for the homogeneous time-dependent Oseen system in $ℝ^{3}$ : spatial decay of the velocity

Paul Deuring (2013)

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We consider the homogeneous time-dependent Oseen system in the whole space $ℝ^{3}$ . The initial data is assumed to behave as $O (| x |^{- 1 - ϵ})$ , and its gradient as $O (| x |^{- 3 / 2 - ϵ})$ , when $| x |$ tends to infinity, where $ϵ$ is a fixed positive number. Then we show that the velocity $u$ decays according to the equation $| u (x, t) | = O (| x |^{- 1})$ , and its spatial gradient $\nabla_{x} u$ decreases with the rate ${| x |}^{- 3 / 2}$ , for $| x |$ tending to infinity, uniformly with respect to the time variable $t$ . Since these decay rates are optimal even in the stationary case, they should also be...