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Isolated zeros for Brownian motion with variable drift by Antunović, Tonći; Burdzy, Krzysztof; Peres, Yuval; Ruscher, Julia is a scholarly article available to read on EtoBox.

What is Isolated zeros for Brownian motion with variable drift about?

It is well known that standard one-dimensional Brownian motion B(t) has no isolated zeros almost surely. We show that for any alpha<1/2 there are alpha-H\"older continuous functions f for which the process B-f has isolated zeros with positive probability. We also prove that for any continuous function f, the zero set of B-f has Hausdorff dimension at least 1/2 with positive probability, and 1/2 is an upper bound if f is 1/2-H\"older continuous or of bounded variation.

Author

Antunović, Tonći; Burdzy, Krzysztof; Peres, Yuval; Ruscher, Julia

Published

2010

Language

EN