Local maxima of two dependent Brownian Motions never coincide
E.A. Cator
TL;DR
This paper proves that two dependent Brownian motions with possibly different drifts almost surely do not share a simultaneous local maximum, using a result on cone points of 2D Brownian motion.
Contribution
It establishes a novel probabilistic result about the non-coincidence of local maxima in dependent Brownian motions with different drifts.
Findings
No simultaneous local maxima occur with probability one
Application of le Gall's cone points result to dependent Brownian motions
Extension of Brownian motion theory to dependent processes with drift
Abstract
We consider two dependent Brownian motions with (possibly) different drift, and apply a result by le Gall on cone points of two dimensional Brownian motion to show that with probability one, there will not be a time that is a local maximum for both processes.
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Taxonomy
TopicsStochastic processes and financial applications · Stochastic processes and statistical mechanics · Financial Risk and Volatility Modeling