Abstract
A local limit theorem for convergence of probability density functions is provided as a tool for the computation of hitting time distributions for Brownian motion, with or without drift, as a limit of hitting times for random walk, and other asymptotic limit theorems of this nature.
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Notes
- 1.
See BCPT pp. 14–15.
- 2.
See Feller (1971), p. 431.
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Bhattacharya, R., Waymire, E.C. (2021). First Passage Time Distributions for Brownian Motion with Drift and a Local Limit Theorem. In: Random Walk, Brownian Motion, and Martingales. Graduate Texts in Mathematics, vol 292. Springer, Cham. https://doi.org/10.1007/978-3-030-78939-8_16
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DOI: https://doi.org/10.1007/978-3-030-78939-8_16
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