Levy's second arcsine law via the ballot theorem
Helmut H. Pitters
TL;DR
This paper presents a simple, elementary proof of Levy's second arcsine law for Brownian motion using basic properties and the ballot theorem, with extensions to Brownian motion with drift.
Contribution
It offers a new, elementary proof of Levy's second arcsine law utilizing basic tools and extends the result to Brownian motion with drift.
Findings
Elementary proof of Levy's second arcsine law
Extension to Brownian motion with drift
Utilizes basic properties and the ballot theorem
Abstract
We provide a new and elementary proof of Levy's second arcsine law for Brownian motion. The only tools required are basic properties of Brownian motion and Poisson processes, and the ballot theorem. Our proof is readily extended to Brownian motion with drift.
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Taxonomy
TopicsStochastic processes and financial applications · stochastic dynamics and bifurcation · Random Matrices and Applications