Our online platform, Wiley Online Library () is one of the world’s most extensive multidisciplinary collections of online resources, covering life, health, social and physical sciences, and humanities. With a growing open access offering, Wiley is committed to the widest possible dissemination of and access to the content we publish and supports all sustainable models of access. Numerical experiments showed the good performance of the stylized model in estimating risk for the Variance Gamma process and the Normal Inverse Gaussian. Wiley has partnerships with many of the world’s leading societies and publishes over 1,500 peer-reviewed journals and 1,500+ new books annually in print and online, as well as databases, major reference works and laboratory protocols in STMS subjects. In this paper, we present the testing of four hypotheses on two streams of observations that are driven by Lévy processes. Wiley has published the works of more than 450 Nobel laureates in all categories: Literature, Economics, Physiology or Medicine, Physics, Chemistry, and Peace. has been a valued source of information and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations. Our core businesses produce scientific, technical, medical, and scholarly journals, reference works, books, database services, and advertising professional books, subscription products, certification and training services and online applications and education content and services including integrated online teaching and learning resources for undergraduate and graduate students and lifelong learners. Mean-field reflected backward stochastic. Peskir and Shiryaev (2000) solved theproblem in (1.3,1.4) when the Poisson processXissimple. Papers listed here are not updated during the production process and are removed once an issue is published. If we can find that you are disabled or not disabled at a step, we make our determination or decision and we do not go on to the next step. See paragraph (h) of this section for an exception to this rule. The sequential evaluation process is a series of five steps that we follow in a set order. Thus, optimal stopping rules in the constrained case qualitatively differ from optimal rules in the unconstrained case.Wiley is a global provider of content and content-enabled workflow solutions in areas of scientific, technical, medical, and scholarly research professional development and education. Special problems of sequential testing for compound Poisson processes have been studiedby Peskir and Shiryaev (2000) and Gapeev (2002). (4) The five-step sequential evaluation process. In contrast to the unconstrained case, optimal stopping rules, in general, cannot be found among interval exit times. Stopping at the intermediate point means that the testing is abandoned without accepting H 0 or H 1. We impose an expectation constraint on the stopping rules allowed and show that an optimal stopping rule satisfying the constraint can be found among the rules of the following type: stop if the posterior probability for H 1 attains a given lower or upper barrier or stop if the posterior probability comes back to a fixed intermediate point after a sufficiently large excursion. ** Corresponding author: study a stopping problem arising from a sequential testing of two simple hypotheses H 0 and H 1 on the drift rate of a Brownian motion. TU Wien, Institute of Statistics and Mathematical Methods in Economics, Institute for Mathematics, University of Jena,
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