اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA Geometric Approach for Bounding Average Stopping Time
240
0
0.0
(
0
)
تأليف
Xinjia Chen
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We propose a geometric approach for bounding average stopping times for stopped random walks in discrete and continuous time. We consider stopping times in the hyperspace of time indexes and stochastic processes. Our techniques relies on exploring geometric properties of continuity or stopping regions. Especially, we make use of the concepts of convex sets and supporting hyperplane. Explicit formulae and efficiently computable bounds are obtained for average stopping times. Our techniques can be applied to bound average stopping times involving random vectors, nonlinear stopping boundary, and constraints of time indexes. Moreover, we establish a stochastic characteristic of convex sets and generalize Jensens inequality, Walds equations and Lordens inequality, which are useful for investigating average stopping times.
قيم البحث
اقرأ أيضاً
Consider the empirical measure, $hat{mathbb{P}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $mathbb{P}$ on the unit interval. For fixed $mathbb{P}$ the Wasserstein distance between $hat{mathbb{P}}_N$ and $mathbb{P}$ is a
random variable on the sample space $[0,1]^N$. Our main result is that its normalised quantiles are asymptotically maximised when $mathbb{P}$ is a convex combination between the uniform distribution supported on the two points ${0,1}$ and the uniform distribution on the unit interval $[0,1]$. This allows us to obtain explicit asymptotic confidence regions for the underlying measure $mathbb{P}$. We also suggest extensions to higher dimensions with numerical evidence.
In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as well as ran
dom problem horizons. The proposed framework is based on a reduction of the original selection problem to one of optimal stopping for a sequence of judiciously constructed independent random variables. We demonstrate that our approach allows exact and efficient computation of optimal policies and various performance metrics thereof for a variety of sequential selection problems, several of which have not been solved to date.
A new expression as a certain asymptotic limit via discrete micro-states of permutations is provided to the mutual information of both continuous and discrete random variables.
Possible reasons for the uniqueness of the positive geometric law in the context of stability of random extremes are explored here culminating in a conjecture characterizing the geometric law. Our reasoning comes closer in justifying the geometric la
w in similar contexts discussed in Arnold et al. (1986) and Marshall & Olkin (1997) and also supplement their arguments.
This article is concerned with the design and analysis of discrete time Feynman-Kac particle integration models with geometric interacting jump processes. We analyze two general types of model, corresponding to whether the reference process is in con
tinuous or discrete time. For the former, we consider discrete generation particle models defined by arbitrarily fine time mesh approximations of the Feynman-Kac models with continuous time path integrals. For the latter, we assume that the discrete process is observed at integer times and we design new approximation models with geometric interacting jumps in terms of a sequence of intermediate time steps between the integers. In both situations, we provide non asymptotic bias and variance theorems w.r.t. the time step and the size of the system, yielding what appear to be the first results of this type for this class of Feynman-Kac particle integration models. We also discuss uniform convergence estimates w.r.t. the time horizon. Our approach is based on an original semigroup analysis with first order decompositions of the fluctuation errors.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
