Exploring new probability density functions related to Brownian local time

This work introduces a new family of probability density functions constructed from 𝐄[𝐿𝐵(1, 𝑥)], the expectation of the Brownian local time 𝐿𝐵(1, 𝑥) at time one. The proposed framework builds probabilistic models directly from local time - a pathwise quantity rarely exploited in density construction...

Full description

Bibliographic Details

Published in:	Kuwait Journal of Science
Main Authors:	Omar Allaoui, Aissa Sghir, Mohamed Mellouk, Mhamed Eddahbi
Format:	Article
Language:	English
Published:	Elsevier 2026-01-01
Subjects:	brownian motion local time occupation density formula standard normal distribution standard gamma distribution cumulative distribution function characteristic function incomplete gamma functions
Online Access:	https://www.sciencedirect.com/science/article/pii/S2307410825001518