主講者: | 1.李增滬教授 (Beijing Normal University, China) 2.洪文明教授 (Beijing Normal University, China) |
講題: | 1.Strong solutions for stochastic equations driven by Levy processes 2.Branching structure for random walk in random environment with bounded jumps and its applications |
時間: | 2010-10-04 (Mon.) 14:10 - 17:00 |
地點: | 數學所 722 研討室 (台大院區) |
Abstract: | Abstract 1: General stochastic equations of non-negative processes with jumps are studied. We provide criteria for the strong existence and uniqueness of solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by spectrally positive Levy processes. Abstract 2:By decomposing the trajectory of the random walk, we reveal a branching structure within the (L,1)-random walk in random environment, which is a multitype branching process with immigration in random environment. We give two applications of the branching structure. Firstly, we specify the explicit invariant density for the Markov chain of ``the environment viewed from the particle" and reprove the law of large numbers of the random walk by a method different with the one used in Br\'{e}mont(2002). Secondly, the branching structure enables us to prove a stable limit law, generalizing the result of Kesten-Kozlov-Spitzer(1975) for the nearest random walk in random environment. The branching structure within the (1,R)-random walk in random environment has been obtained as well. The (L,R)-random walk means that the possible jump range by the walk to the left is L and to the right is R. This is a joint walk with Huaming Wang and Lin Zhang.(arXiv:1003.3731 and arXiv:1003.3733 ) |
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