An isonormal process associated with a Brownian motion




Brownian motion, self-intersection local time, Gaussian random field


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.

Cuzick, J. & DuPreez, J. P. (1982). Joint continuity of Gaussian local times. Ann. Probab., 10, No. 3, pp. 810-817.



How to Cite

Dorogovtsev А. ., & Nishchenko І. . (2022). An isonormal process associated with a Brownian motion. Reports of the National Academy of Sciences of Ukraine, (6), 10–16.