DIVERGENCE RESULTS FOR SELF-INTERSECTION LOCAL TIMES OF GAUSSIAN ${\mathscr S}' ({\mathbb R}^d)$-PROCESSES-Reference-Cited by-同舟云学术

DIVERGENCE RESULTS FOR SELF-INTERSECTION LOCAL TIMES OF GAUSSIAN ${\mathscr S}' ({\mathbb R}^d)$-PROCESSES

Published:2001-12 Issue:04 Volume:04 Page:417-488
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

TALARCZYK ANNA¹

Affiliation:

1. Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warszawa, Poland

Abstract

For various types of Gaussian [Formula: see text]-processes we consider the case when the self-intersection local time (SILT) does not exist. We study the rate of divergence of the corresponding approximating processes obtaining, after suitable normalizations convergence in law to some [Formula: see text]-valued processes (not necessarily Gaussian). We also obtain some new necessary conditions for the existence of SILT. We give examples associated with fluctuation limits of α-stable particle systems.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025701000668

Reference3 articles.

1. Intersection Local Times for Infinite Systems of Brownian Motions and for the Brownian Density Process

2. Intersection Local Times of All Orders for Brownian and Stable Density Processes--Construction, Renormalisation and Limit Laws

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