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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2023 Volume 525, Pages 30–50 (Mi znsl7366)

The second order local time of the Bessel process at the moment inverse to local time

A. N. Borodin

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: According to the Ray–Knight description the Bessel local time at the moment inverse to local time is a diffusion process with respect to space parameter. This diffusion has a local time. Thus, we come to the definition of the local time of the original Bessel local time. We will call such a process the Bessel local time of the second order at the moment, inverse to local time. The paper studies the Laplace transform of the distribution of the second order Bessel local time.

Key words and phrases: Bessel local time, moment inverse to local time, second order local time, local time distribution.

Received: 17.09.2023



© Steklov Math. Inst. of RAS, 2024