4,239 research outputs found
Constructing Dynamic Treatment Regimes in Infinite-Horizon Settings
The application of existing methods for constructing optimal dynamic
treatment regimes is limited to cases where investigators are interested in
optimizing a utility function over a fixed period of time (finite horizon). In
this manuscript, we develop an inferential procedure based on temporal
difference residuals for optimal dynamic treatment regimes in infinite-horizon
settings, where there is no a priori fixed end of follow-up point. The proposed
method can be used to determine the optimal regime in chronic diseases where
patients are monitored and treated throughout their life. We derive large
sample results necessary for conducting inference. We also simulate a cohort of
patients with diabetes to mimic the third wave of the National Health and
Nutrition Examination Survey, and we examine the performance of the proposed
method in controlling the level of hemoglobin A1c. Supplementary materials for
this article are available online
Enlargements of filtrations and path decompositions at non-stopping times
Az\'{e}ma associated with an honest time L the supermartingale
and established some of its
important properties. This supermartingale plays a central role in the general
theory of stochastic processes and in particular in the theory of progressive
enlargements of filtrations. In this paper, we shall give an additive
characterization for these supermartingales, which in turn will naturally
provide many examples of enlargements of filtrations. In particular, we use
this characterization to establish some path decomposition results, closely
related to or reminiscent of Williams' path decomposition results.Comment: New titlle for this second version; Typos corrected; same as the
published version in Prob. Theory and Related Fields 136 (4), 2006, 524-54
A class of remarkable submartingales
In this paper, we consider the special class of positive local submartingales
(X_{t}) of the form: X_{t}=N_{t}+A_{t}, where the measure (dA_{t}) is carried
by the set {t: X_{t}=0}. We show that many examples of stochastic processes
studied in the literature are in this class and propose a unified approach
based on martingale techniques to study them. In particular, we establish some
martingale characterizations for these processes and compute explicitly some
distributions involving the pair (X_{t},A_{t}). We also associate with X a
solution to the Skorokhod's stopping problem for probability measures on the
positive half-line.Comment: Typos corrected. Close to the published versio
An essay on the general theory of stochastic processes
This text is a survey of the general theory of stochastic processes, with a
view towards random times and enlargements of filtrations. The first five
chapters present standard materials, which were developed by the French
probability school and which are usually written in French. The material
presented in the last three chapters is less standard and takes into account
some recent developments.Comment: Published at http://dx.doi.org/10.1214/154957806000000104 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
An Efficient Thread Mapping Strategy for Multiprogramming on Manycore Processors
The emergence of multicore and manycore processors is set to change the
parallel computing world. Applications are shifting towards increased
parallelism in order to utilise these architectures efficiently. This leads to
a situation where every application creates its desirable number of threads,
based on its parallel nature and the system resources allowance. Task
scheduling in such a multithreaded multiprogramming environment is a
significant challenge. In task scheduling, not only the order of the execution,
but also the mapping of threads to the execution resources is of a great
importance. In this paper we state and discuss some fundamental rules based on
results obtained from selected applications of the BOTS benchmarks on the
64-core TILEPro64 processor. We demonstrate how previously efficient mapping
policies such as those of the SMP Linux scheduler become inefficient when the
number of threads and cores grows. We propose a novel, low-overhead technique,
a heuristic based on the amount of time spent by each CPU doing some useful
work, to fairly distribute the workloads amongst the cores in a
multiprogramming environment. Our novel approach could be implemented as a
pragma similar to those in the new task-based OpenMP versions, or can be
incorporated as a distributed thread mapping mechanism in future manycore
programming frameworks. We show that our thread mapping scheme can outperform
the native GNU/Linux thread scheduler in both single-programming and
multiprogramming environments.Comment: ParCo Conference, Munich, Germany, 201
- …