Some properties of stochastic differential equation on L′evy processes with non-Lipschitz coefficients
Date Issued
2007
Date
2007
Author(s)
Lin, Ching-Yao
Abstract
We shall discauss three properties of stochastic differential equation on Lèvy processes. One is the existence of the strong solutions of stochastic differential equation on Lèvy processes with non-Lipschitz conditions, the diffusion case with non-Lipschitz conditions have been studied by Shizan Fang and Tusheng Zhang [1]. Second subject is that we would generalize to the dependence of the solutions with respect to the initial values with Lévy processes.(The results are discussed by Shizan Fang and Tusheng Zhang [1] with diffusion cases) The third is the comparison theorem that says that there are two stochastic differential equation on Lèvy processes with different drift terms and we can compare the solutions by the two drift terms. The comparison theorem with diffusion case have studied by Ikeda and Watanabe [3].
Subjects
L′evy processes
stochastic differential equation on L′evy processes
Type
thesis
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