R. Bass

activity

19932023

most citedBrownian motion on the Sierpinski carpet

69 citations · 275 across the 36 of their papers we have counts for

collaborators

38 papers

math.PR2023

The supremum of Brownian local times on Hölder curves, II

Richard F. Bass, Krzysztof Burdzy

For $f : [0, 1] \to R$ , we consider $L_{t}^{f}$ , the local time of space-time Brownian motion on the curve $f$ . Let $S_{α}$ be the class of all functions whose Hölder norm of…

math.PR2020★ 59 cited

Stability of parabolic Harnack inequalities on metric measure spaces

M. T. Barlow, R. F. Bass, T. Kumagai

Let $(X, d, μ)$ be a metric measure space with a local regular Dirichlet form. We give necessary and sufficient conditions for a parabolic Harnack inequality with global space-time s…

math.PR2013

The rate of escape of the most visited site of Brownian motion

Richard F. Bass

Let ${L_{t}^{z}}$ be the jointly continuous local times of a one-dimensional Brownian motion and let $L_{t}^{*} = sup_{z \in R} L_{t}^{z}$ . Let $V_{t}$ be any point $z$ such that $L^z_t=…

math.PR2012

A stochastic differential equation with a sticky point

Richard F. Bass

We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathw…

math.PR2012

Harnack inequalities in infinite dimensions

Richard F. Bass, Maria Gordina

We consider the Harnack inequality for harmonic functions with respect to three types of infinite dimensional operators. For the infinite dimensional Laplacian, we show no Harnack…

math.FA2012

Meyers inequality and strong stability for stable-like operators

Richard F. Bass, Hua Ren

Let $α \in (0, 2)$ , let $E (u, u) = \int_{R^{d}} \int_{R^{d}} (u (y) - u (x))^{2} \frac{A ( x , y )}{∣ x - y ∣ ^{d + α}} d y d x$ be the Dirichlet form for a stable-like operator, let $$Γu(…