An isonormal process associated with a Brownian motion
DOI:
https://doi.org/10.15407/dopovidi2022.06.010Keywords:
Brownian motion, self-intersection local time, Gaussian random fieldAbstract
In the article a new method for studying the properties of trajectories of a standard planar Brownian motion {B(t ); t ≥ 0} is proposed. The approach is as follows. The superposition of a stationary Gaussian field, that does not depend on B , with the process B itself is considered. The existence of local times and self-intersection local times of the obtained stationary process depends on the convergence of some multidimensional integrals along the trajectories of the Brownian motion B .
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Geman, D., Horowitz, J. & Rosen, J. (1984). A local time analysis of intersections of Brownian paths in the plane. Ann. Probab., 12, No. 1, pp. 86-107. https://doi.org/10.1214/aop/1176993375
Cuzick, J. & DuPreez, J. P. (1982). Joint continuity of Gaussian local times. Ann. Probab., 10, No. 3, pp. 810-817. https://doi.org/10.1214/aop/1176993789
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