9 citations · 24 across the 24 of their papers we have counts for
22 papers · 1 filter
Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths: The correlated case
Soukaina Douissi, Philip Ernst, Frederi Viens
We study the continuous-time version of the empirical correlation coefficient between the paths of two possibly correlated Ornstein-Uhlenbeck processes, known as Yule's nonsense co…
Exact expressions for the maximal probability that all -wise independent bits are 1
Daniel Berend, Philip A. Ernst, Aryeh Kontorovich +1
Let denote the maximum probability of the event under a -wise independent distribution whose marginals are Bernoulli random variables w…
The Gapeev-Shiryaev Conjecture
Philip A. Ernst, Goran Peskir
The Gapeev-Shiryaev conjecture (originating in Gapeev and Shiryaev (2011) and Gapeev and Shiryaev (2013)) can be broadly stated as follows: Monotonicity of the signal-to-noise rati…
Asymptotic optimality of dynamic first-fit packing on the half-axis
Philip A. Ernst, Alexander L. Stolyar, Jixin Wang
We revisit a classical problem in dynamic storage allocation. Items arrive in a linear storage medium, modeled as a half-axis, at a Poisson rate and depart after an independent…
Quickest Real-Time Detection of Multiple Brownian Drifts
Philip A. Ernst, Hongwei Mei, Goran Peskir
Consider the motion of a Brownian particle in dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservab…
Exact optimal stopping for multidimensional linear switching diffusions
Philip Ernst, Hongwei Mei
The paper studies a class of multidimensional optimal stopping problems with infinite horizon for linear switching diffusions. There are two main novelties in the optimal problems…
On the diameter of the stopped spider process
Ewelina Bednarz, Philip A. Ernst, Adam Osekowski
We consider the Brownian ``spider process'', also known as Walsh Brownian motion, first introduced in the epilogue of Walsh 1978. The paper provides the best constant for the…
The least favorable noise
Philip A. Ernst, Abram M. Kagan, L. C. G. Rogers
Suppose that a random variable of interest is observed perturbed by independent additive noise . This paper concerns the "the least favorable perturbation" $\hat Y_\ep$, whi…
Yule's "nonsense correlation" for Gaussian random walks
Philip A. Ernst, Dongzhou Huang, Frederi G. Viens
The purpose of this paper is to provide an exact formula for the second moment of the empirical correlation of two independent Gaussian random walks as well as implicit formulas fo…
Escape and absorption probabilities for obliquely reflected Brownian motion in a quadrant
Philip Ernst, Sandro Franceschi, Dongzhou Huang
We consider an obliquely reflected Brownian motion with positive drift in a quadrant stopped at time , where is the first hitting time of th…
Quickest Real-Time Detection of a Brownian Coordinate Drift
Philip A. Ernst, Goran Peskir
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/un…
Asymptotic behavior of the occupancy density for obliquely reflected Brownian motion in a half-plane and Martin boundary
Philip Ernst, Sandro Franceschi
Let be the occupancy density of an obliquely reflected Brownian motion in the half plane and let (, ) be the polar coordinates of a point in the upper half plane. This wo…
The rencontre problem
F. Thomas Bruss, Philip A. Ernst, Dongzhou Huang
Let be independent sequences of Bernoulli random v…
Optimal real-time detection of a drifting Brownian coordinate
Philip Ernst, Goran Peskir, Quan Zhou
Consider the motion of a Brownian particle in three dimensions, whose two spatial coordinates are standard Brownian motions with zero drift, and the remaining (unknown) spatial coo…
MEXIT: Maximal un-coupling times for stochastic processes
P. A. Ernst, W. S. Kendall, G. O. Roberts +1
Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this pa…
Stability and busy periods in a multiclass queue with state-dependent arrival rates
Philip Ernst, Søren Asmussen, John Hasenbein
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in…
Asymptotics for the Time of Ruin in the War of Attrition
Philip Ernst, Ilie Grigorescu
We consider two players, starting with and units, respectively. In each round, the winner is decided with probability proportional to each player's fortune, and the opponen…
Exercising Control When Confronted by a (Brownian) Spider
Philip Ernst
We consider the Brownian "spider," a construct introduced in \cite{Dubins} and in \cite{Pitman}. In this note, the author proves the "spider" bounds by using the dynamic programmin…
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…
The value of foresight
Philip Ernst, L. C. G. Rogers, Quan Zhou
Suppose you have one unit of stock, currently worth 1, which you must sell before time . The Optional Sampling Theorem tells us that whatever stopping time we choose to sell, th…
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…
On the Time for Brownian Motion to Visit Every Point on a Circle
Philip Ernst, Larry Shepp
Consider a Wiener process on a circle of circumference . We prove the rather surprising result that the Laplace transform of the distribution of the first time, , when…