32 research outputs found
A note on the central limit theorem for a one-sided reflected Ornstein-Uhlenbeck process
In this short communication we present a (functional) central limit theorem
for the idle process of a one-sided reflected Ornstein-Uhlenbeck proces
Minimising MCMC variance via diffusion limits, with an application to simulated tempering
We derive new results comparing the asymptotic variance of diffusions by
writing them as appropriate limits of discrete-time birth-death chains which
themselves satisfy Peskun orderings. We then apply our results to simulated
tempering algorithms to establish which choice of inverse temperatures
minimises the asymptotic variance of all functionals and thus leads to the most
efficient MCMC algorithm.Comment: Published in at http://dx.doi.org/10.1214/12-AAP918 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
One-dimensional reflected diffusions with two boundaries and an inverse first-hitting problem
We study an inverse first-hitting problem for a one-dimensional,
time-homogeneous diffusion reflected between two boundaries and
which starts from a random position Let be a given
threshold, such that and an assigned distribution
function. The problem consists of finding the distribution of such that
the first-hitting time of to has distribution This is a
generalization of the analogous problem for ordinary diffusions, i.e. without
reflecting, previously considered by the author
On the generalized drift Skorokhod problem in one dimension
We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein–Uhlenbeck (OU) process to the first hitting time distribution of an OU process (that is not reflected). Then, we use this relationship to approximate the transient distribution of the GI/GI/1 + GI queue in conventional heavy traffic and the M/M/N/N queue in a many-server heavy traffic regime
The impact of reneging in processor sharing queues
We investigate an overloaded processor sharing queue with renewal arrivals and generally distributed service times. Impatient customers may abandon the queue, or renege, before completing service. The random time representing a customer’s patience has a general distribution and may be dependent on his initial service time requirement. We propose a scaling procedure that gives rise to a fluid model, with nontrivial yet tractable steady state behavior. This fluid model captures many essential features of the underlying stochastic model, and we use it to analyze the impact of impatience in processor sharing queues. We show that this impact can be substantial compared with FCFS, and we propose a simple admission control policy to overcome these negative impacts