71 citations · 78 across the 7 of their papers we have counts for
11 papers
Yule's "Nonsense Correlation" Solved!
Philip Ernst, Larry Shepp, Abraham Wyner
In this paper, we resolve a longstanding open statistical problem. The problem is to mathematically confirm Yule's 1926 empirical finding of "nonsense correlation" (\cite{Yule}). W…
On Optimal Retirement (How to Retire Early)
Philip Ernst, Dean Foster, Larry Shepp
We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function and our current net worth as for any , we invest…
Revisiting a Theorem of L.A. Shepp on Optimal Stopping
Philip Ernst, Larry Shepp
Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel…
On occupation times of the first and third quadrants for planar Brownian motion
Philip Ernst, Larry Shepp
An open problem of interest, first infused into the applied probability community in the work of Bingham and Doney in 1988, (see \cite{Bingham}) is stated as follows: find the dist…
Fiscal stimulus as an optimal control problem
Philip A. Ernst, Michael B. Imerman, Larry Shepp +1
During the Great Recession, Democrats in the United States argued that government spending could be utilized to "grease the wheels" of the economy in order to create wealth and to…
The General Stationary Gaussian Markov Process
Larry Brown, Philip Ernst, Larry Shepp +1
We find the class, , of all zero mean stationary Gaussian processes, with derivatives, for which \begin{equation} Z(t) \equiv (Y^{(0…