scholarly journals Asymptotic equivalence for pure jump Lévy processes with unknown Lévy density and Gaussian white noise

2016 ◽  
Vol 126 (2) ◽  
pp. 503-541 ◽  
Author(s):  
Ester Mariucci
Keyword(s):  
White Noise ◽  
Lévy Processes ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Asymptotic Equivalence ◽  
Lévy Density

On modelling physical systems with stochastic models: diffusion versus Lévy processes

2008 ◽  
Vol 366 (1875) ◽  
pp. 2455-2474 ◽  
Author(s):  
Cécile Penland ◽  
Brian D Ewald
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Lévy Processes ◽  
Numerical Models ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Physical Systems ◽  
Random Forcing ◽  
Weather And Climate ◽  
Made In

Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

scholarly journals White noise analysis for Lévy processes

2004 ◽  
Vol 206 (1) ◽  
pp. 109-148 ◽  
Author(s):  
Giulia Di Nunno ◽  
Bernt Øksendal ◽  
Frank Proske
Keyword(s):  
White Noise ◽  
Lévy Processes ◽  
Noise Analysis ◽  
Levy Processes ◽  
White Noise Analysis

scholarly journals Local asymptotic equivalence of pure states ensembles and quantum Gaussian white noise

2018 ◽  
Vol 46 (6B) ◽  
pp. 3676-3706
Author(s):  
Cristina Butucea ◽  
Mădălin Guţă ◽  
Michael Nussbaum
Keyword(s):  
White Noise ◽  
Gaussian White Noise ◽  
Asymptotic Equivalence ◽  
Pure States

scholarly journals Infinite dimensional analysis of pure jump Lévy processes on the Poisson space

2006 ◽  
Vol 98 (2) ◽  
pp. 237 ◽  
Author(s):  
Arne Løkka ◽  
Frank Norbert Proske
Keyword(s):  
White Noise ◽  
Lévy Processes ◽  
Levy Processes ◽  
Wick Product ◽  
Charlier Polynomials ◽  
Starting Point ◽  
Poisson Space ◽  
Lévy Measures ◽  
Distribution Spaces ◽  
White Noise Calculus

We develop a white noise calculus for pure jump Lévy processes on the Poisson space. This theory covers the treatment of Lévy processes of unbounded variation. The starting point of the theory is the construction of a distribution space. This space has many of the same nice properties as the classical Schwartz space, but is modified in a certain way in order to be more suitable for pure jump Lévy processes. We apply Minlos's theorem to this space and obtain a white noise measure which satisfies the first condition of analyticity, and which is non-degenerate. Furthermore, we obtain generalized Charlier polynomials for all Lévy measures. We introduce Kondratiev test function and distribution spaces, the $\mathcal{S}$-transform and the Wick product. We proceed by using a transfer principle on Poisson spaces to establish a differential calculus.

scholarly journals Lévy processes and Lévy white noise as tempered distributions

2017 ◽  
Vol 45 (6B) ◽  
pp. 4389-4418 ◽  
Author(s):  
Robert C. Dalang ◽  
Thomas Humeau
Keyword(s):  
White Noise ◽  
Lévy Processes ◽  
Levy Processes ◽  
Tempered Distributions ◽  
Lévy White Noise
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