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 $Z_{t}^{L}=\mathbb{P}[L>t|\mathcal{F}_{t}]$ 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