Topic
Stopped process
About: Stopped process is a research topic. Over the lifetime, 42 publications have been published within this topic receiving 588 citations.
Papers
TL;DR: In this paper, the authors solve the Skorokhod embedding problem for a general time-homogeneous diffusion, and derive necessary and sufficient conditions under which there exists a bounded embedding.
Abstract: We solve the Skorokhod embedding problem (SEP) for a general time-homogeneous diffusion X: given a distribution \rho, we construct a stopping time T such that the stopped process X_T has the distribution \rho? Our solution method makes use of martingale representations (in a similar way to Bass [3] who solves the SEP for Brownian motion) and draws on law uniqueness of weak solutions of SDEs.
Then we ask if there exist solutions of the SEP which are respectively finite almost surely, integrable or bounded, and when does our proposed construction have these properties. We provide conditions that guarantee existence of finite time solutions. Then, we fully characterize the distributions that can be embedded with integrable stopping times. Finally, we derive necessary, respectively sufficient, conditions under which there exists a bounded embedding.
28 citations
Patent•
IBM1
TL;DR: In this article, a method for investigating the operation of processes of an application program running on a multitasking operating system of a computer system to determine if any of the processes have stopped for a predetermined exception incident, by identifying to the operating system a plurality of predetermined exceptions to be investigated; instructing said operating system to stop a process when it encounters one of the predetermined exception incidents; scanning the computer system periodically for stopped processes; determining whether a stopped process has been identified as having encountered a predetermined exceptions incident; and performing a predetermined action if the process has encountered a preemptive action
Abstract: The invention provides a method, and a program for investigating the operation of processes of an application program running on a multitasking operating system of a computer system to determine if any of the processes have stopped for a predetermined exception incident, by: identifying to the operating system a plurality of predetermined exceptions to be investigated; instructing said operating system to stop a process when it encounters one of the predetermined exception incidents; scanning the computer system periodically for stopped processes; determining whether a stopped process has been identified as having encountered a predetermined exception incident; and performing a predetermined action if the process has encountered a predetermined exception incident.
26 citations
Journal Article•
TL;DR: This paper deals with sensitivity analysis (gradient estimation) of random horizon cost functions of Markov chains and provides a general condition under which the gradient of the random horizon performance can be obtained in a closed form expression.
Abstract: This paper deals with sensitivity analysis (gradient estimation) of random horizon cost functions of Markov chains. More precisely, we consider general state-space Markov chains and the random horizon is given through a hitting time of the chain onto a predened set. The \cost" of interest is an expectation of a functional of the stopped process. This encompasses a wide range of models, such as the Gambler's ruin problem and performance evaluation for stationary queueing networks. We work within the framework of measure-valued dieren tiation and provide a general condition under which the gradient of the random horizon performance can be obtained in a closed form expression. For several scenarios, which occur typically in applications, we subsequently provide sucien t conditions for our general condition to hold. We illustrate our results with a series of examples. Eventually, we discuss unbiased sensitivity estimators and establish a new unbiased estimator for the gradient of stationary Markov chains.
24 citations
TL;DR: In this article, a stopping time problem for multidimensional stochastic approximation algorithms is studied, and the stopping rule is so determined that the recursive procedure will be terminated if the unknown parameter θ is inside a desired ellipsoidal confidence region with high probability.
17 citations
Posted Content•
TL;DR: In this article, the authors studied the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process and showed that the stopping time also impacts the dynamics of the stopping process through the dependence of the coefficients on the law.
Abstract: We study the optimal stopping problem of McKean-Vlasov diffusions when the criterion is a function of the law of the stopped process. A remarkable new feature in this setting is that the stopping time also impacts the dynamics of the stopped process through the dependence of the coefficients on the law. The mean field stopping problem is introduced in weak formulation in terms of the joint marginal law of the stopped underlying process and the survival process. This specification satisfies a dynamic programming principle. The corresponding dynamic programming equation is an obstacle problem on the Wasserstein space, and is obtained by means of a general Ito formula for flows of marginal laws of cadlag semimartingales. Our verification result characterizes the nature of optimal stopping policies, highlighting the crucial need to randomized stopping. The effectiveness of our dynamic programming equation is illustrated by various examples including the mean-variance and expected shortfall criteria.
17 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 1 |
| 2019 | 2 |
| 2018 | 1 |
| 2017 | 2 |
| 2016 | 3 |