83 citations · 332 across the 13 of their papers we have counts for
13 papers
A first passage problem for a Poisson counting process with a linear moving boundary
Ivan N. Burenev, Michael J. Kearney, Satya N. Majumdar
The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across t…
A note on an absorption problem for a Brownian particle moving in a harmonic potential
Michael J. Kearney, Richard J. Martin
An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When…
Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
Michael J. Kearney, Richard J. Martin
We consider the area functional defined by the integral of an Ornstein-Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium…
On a stochastic version of Lanchester's model of combat
Michael J. Kearney, Richard J. Martin
Lanchester's model of combat has certain deficiencies in its standard form arising from the neglect of the influence of random fluctuations. Several approaches to rectify this have…
Record statistics for a discrete-time random walk with correlated steps
Michael J. Kearney
The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important fea…
Long- and short-time asymptotics of the first-passage time of the Ornstein-Uhlenbeck and other mean-reverting processes
R. J. Martin, M. J. Kearney, R. V. Craster
The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a s…