A formula for the density of local time of the Brox diffusion in a time-window
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Abstract
After leaving fixed the environment of the Brox diffusion, we give explicitly the probability density of the local time of this process at first passage times. The main idea is to use the fact that the Brox diffusion can be written in term of a time change of a standard Brownian motion. Working with a specific stopping times is key.
Acknowledgements
The authors acknowledge the University of Costa Rica and CIMPA. We also thank the anonymous referee for helping to improve the paper.
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Communicated by: Vyacheslav L. Girko
References
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© 2025 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Truncated Euler–Maruyama approximation for solving perturbed stochastic differential equations with reflected boundary
- Nonparametric local linear estimation of the conditional distribution for functional and censored data
- On RBSDELs with time-delayed generators and RCLL obstacle
- Stochastic integral for non-adapted processes with respect to the Rosenblatt process
- A note on Euler approximations for stochastic differential equations involving the local time at point zero
- A formula for the density of local time of the Brox diffusion in a time-window
- Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion with Hurst parameter lesser than 1/2
Artikel in diesem Heft
- Frontmatter
- Truncated Euler–Maruyama approximation for solving perturbed stochastic differential equations with reflected boundary
- Nonparametric local linear estimation of the conditional distribution for functional and censored data
- On RBSDELs with time-delayed generators and RCLL obstacle
- Stochastic integral for non-adapted processes with respect to the Rosenblatt process
- A note on Euler approximations for stochastic differential equations involving the local time at point zero
- A formula for the density of local time of the Brox diffusion in a time-window
- Controllability of neutral stochastic integro-differential evolution equations driven by a fractional Brownian motion with Hurst parameter lesser than 1/2
