Richard F. Bass
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View article: Uniqueness for the Skorokhod problem in an orthant: critical cases
Uniqueness for the Skorokhod problem in an orthant: critical cases Open
Consider the Skorokhod problem in the closed non-negative orthant: find a solution $(g(t),m(t))$ to \[ g(t)= f(t)+ Rm(t),\] where $f$ is a given continuous vector-valued function with $f(0)$ in the orthant, $R$ is a given $d\times d$ matri…
View article: Two results from Mandelbaum's paper: "The dynamic complementarity problem"
Two results from Mandelbaum's paper: "The dynamic complementarity problem" Open
A draft of a paper by Mandelbaum, "The dynamic complementarity problem", was circulated in 1987, but has never been published. We give an exposition of two important results from that paper which are not readily accessible in the literatur…
View article: Pathwise non-uniqueness for Brownian motion in a quadrant with oblique reflection
Pathwise non-uniqueness for Brownian motion in a quadrant with oblique reflection Open
Consider the Skorokhod equation in the closed first quadrant: \[ X_t=x_0+ B_t+\int_0^t{\bf v}(X_s)\, dL_s,\] where $B_t$ is standard 2-dimensional Brownian motion, $X_t$ takes values in the quadrant for all $t$, and $L_t$ is a process that…
View article: The supremum of Brownian local times on Hölder curves, II
The supremum of Brownian local times on Hölder curves, II Open
For $f: [0,1]\to \mathbb R$, we consider $L^f_t$, the local time of space-time Brownian motion on the curve $f$. Let ${\cal S}_α$ be the class of all functions whose Hölder norm of order $α$ is less than or equal to 1. We show that the sup…
View article: The rate of escape of the most visited site of Brownian motion
The rate of escape of the most visited site of Brownian motion Open
Let {Ltz} be the jointly continuous local times of a one-dimensional Brownian motion and let Lt∗=supz∈RLtz. Let Vt be any point z such that Ltz=Lt∗, a most visited site of Brownian motion. We prove that if γ>1, then lim inft→∞ |Vt| t∕(logt…
View article: Types and Applications of P3,0 Seventh-Chord Transformations in Late Nineteenth-Century Music
Types and Applications of P3,0 Seventh-Chord Transformations in Late Nineteenth-Century Music Open
The expression P 3,0 refers to one class of parsimonious voice-leading transformations between seventh chords introduced in a 1998 article by Jack Douthett and Peter Steinbach as P m,n ( Journal of Music Theory 42 (2): 241–63). In addition…