# The spans in Brownian motion

@article{Evans2015TheSI, title={The spans in Brownian motion}, author={Steven N. Evans and Jim Pitman and Wenpin Tang}, journal={Annales De L Institut Henri Poincare-probabilites Et Statistiques}, year={2015}, volume={53}, pages={1108-1135} }

Author(s): Evans, S; Pitman, J; Tang, W | Abstract: © Association des Publications de l'Institut Henri Poincare, 2017. For d ϵ {1, 2, 3}, let (Bdt ; t g 0) be a d-dimensional standard Brownian motion. We study the d-Brownian span set Span(d) := {t - s;Bds = Bdt for some 0 l s l t}. We prove that almost surely the random set Span(d) is α-compact and dense in ℝ+. In addition, we show that Span(1) = ℝ+ almost surely; the Lebesgue measure of Span(2) is 0 almost surely and its Hausdorff dimension is…

## One Citation

### Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

- MathematicsStochastic Analysis and Applications
- 2020

Abstract In a recent paper by Yu (arXiv:2008.05633, 2020), higher order derivatives of self-intersection local time of fractional Brownian motion were defined, and existence over certain regions of…

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