演講者：李育嘉教授

單　位：國立高雄大學應用數學系

日　期：2011年3月16日　PM 14:30

地　點：國立高雄大學理學院408室

講　題：A Characterization of Levy White Noise Measures

摘　要：

Being inspired by the observation that the Stein's identity is closely connected to the quantum decomposition of probability measures [3] and the Segal-Bargmann transform [2], we are able to characterize the Lévy white noise measures on the space S' of tempered distributions associated with a Lévy spectrum having finite second moment. The results not only extends the Stein [4] and Chen's lemma [1] for Gaussian and Poisson distributions to infinite dimensions but also to many other infinitely divisible distributions such as Gamma and Pascal distributions and corresponding Lévy white noise measures on S'. 

References

[1] A. D. Barbour, L. H. Y. Chen, An Introduction to Stein's Method, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 4, Singapore University Press, World  Scienti_c, Singapore, 2005.
[2] Y.-J. Lee, H.-H. Shih, The Segal-Bargmann transform for Lévy functionals, J. Funct. Anal. 168 (1999) 46-83. 
[3] Y.-J. Lee, H.-H. Shih, Analysis of generalized Lévy white noise functionals, J. Funct. Anal.211 (2004) 1-70.
[4] C. Stein, Approximation Computation of Expectations, Institute of Mathematical Statistics Lecture Notes, Monograph Series, Vol. 7, Institute of Mathematical Statistics, Hayward, CA, 1986.