scholarly journals Analysis of generalized Lévy white noise functionals

2004 ◽  
Vol 211 (1) ◽  
pp. 1-70 ◽  
Author(s):  
Yuh-Jia Lee ◽  
Hsin-Hung Shih
Keyword(s):  
White Noise ◽  
Lévy White Noise ◽  
White Noise Functionals

GENERALIZED FRACTIONAL LÉVY PROCESSES: A WHITE NOISE APPROACH

2006 ◽  
Vol 06 (04) ◽  
pp. 473-485 ◽  
Author(s):  
ZHI YUAN HUANG ◽  
PEI YAN LI
Keyword(s):  
White Noise ◽  
Lévy Processes ◽  
Sufficient Conditions ◽  
Levy Processes ◽  
Simple Condition ◽  
Lévy Measure ◽  
Lévy White Noise ◽  
White Noise Functionals

In this paper, with a simple condition on Lévy measure, we construct the (tempered) generalized fractional Lévy processes (GFLP) as Lévy white noise functionals and investigate their distribution and sample properties through this white noise approach. We also give some sufficient conditions under which the usual fractional Lévy processes (FLP) are well defined.

scholarly journals Infinite dimensional rotations and Laplacians in terms of white noise calculus

1992 ◽  
Vol 128 ◽  
pp. 65-93 ◽  
Author(s):  
Takeyuki Hida ◽  
Nobuaki Obata ◽  
Kimiaki Saitô
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Quantum Physics ◽  
Variational Calculus ◽  
Rotation Group ◽  
Infinite Dimensional ◽  
Lévy Laplacian ◽  
White Noise Functionals ◽  
White Noise Calculus

The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.

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