【摘 要】
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In this paper, at first, we obtain a necessary condition of H -càdlàg modification and H -weakly càdlàg modification of generalized Ornstein-Uhlenbeck p
【出 处】
：
2015 Peking University Youth Probability Forum(2015年北京大学青年概率
论文部分内容阅读
In this paper, at first, we obtain a necessary condition of H -càdlàg modification and H -weakly càdlàg modification of generalized Ornstein-Uhlenbeck processes with Lévy noises in Hilbert spaces H . And then, we give a necessary and sufficient condition of H -càdlàg modification and H -weakly càdlàg modification of Ornstein-Uhlenbeck processes driven by cylindrical α -semi-stable processes. Secondly, we investigate the properties of cylindrical càdlàg modification and V -cylindrical càdlàg modification. Applying the obtained results to the diagonal Ornstein-Uhlenbeck processes with α -stable noises, we show a necessary and sufficient condition of cylindrical càdlàg modification and V -cylindrical càdlàg modification in symmetric case for α∈(0,1) , and give a sufficient condition in general case for α∈(0,2) . Some examples illustrate the relations among the concepts of various càdlàg modification.
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