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作者：BERTOIN, J
摘要：Let G = (G(t), t greater than or equal to 0) be the process of last passage times at some fixed point of a Markov process. The Dynkin-Lamperti theorem provides a necessary and sufficient condition for G(t)/t to converge in law as t --> infinity to some non-degenerate limit (which is then a generalized arcsine law). Under this condition, we give a simple integral test that characterizes the lower-functions of G. We obtain a similar result for A(+) = (A(+)(t),t greater than or equal to 0), the t...
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作者：HU, Y; SHI, Z
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：Let {W(t); 0 less than or equal to t less than or equal to 1} be a two-dimensional Wiener process starting from 0. We are interested in the almost sure asymptotic behaviour, as r tends to 0, of the processes X(r) and Y(r), where X(r) denotes the total time spent by W in the ball centered at 0 with radius r, and Y(r) the distance between 0 and the curve (W(t); r less than or equal to t less than or equal to 1}. While a characterization of the lower functions of Y was previously established by S...
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作者：GRAHAM, C
摘要：We study a process reflecting in a domain. The process follows Wentzell non-sticky boundary conditions while being adsorbed at the boundary at a certain rate with respect to local time and desorbed at a rate with respect to natural time. We show that when the rates go to infinity with a converging ratio, the process converges to a process with sticky reflection having the limit ratio as the sojourn coefficient. We then study a mean-field interacting system of such particles. We show propagatio...
