An asymptotic property of Gaussian stationary processes

An Asymptotic Property of Gaussian Processes . K 1 )

Stationary Systems of Gaussian Processes

We describe all countable particle systems on R which have the following three properties: independence, Gaussianity, and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson point process with intensity measure m and moving independently of each other according to the law of some Gaussian process ξ. We describe all pairs (m, ξ) generating a s...

asymptotic property of order statistics and sample quntile

چکیده: فرض کنید که تابعی از اپسیلون یک مجموع نامتناهی از احتمالات موزون مربوط به مجموع های جزئی براساس یک دنباله از متغیرهای تصادفی مستقل و همتوزیع باشد، و همچنین فرض کنید توابعی مانند g و h وجود دارند که هرگاه امید ریاضی توان دوم x متناهی و امیدریاضی x صفر باشد، در این صورت می توان حد حاصلضرب این توابع را بصورت تابعی از امید ریاضی توان دوم x نوشت. حالت عکس نیز برقرار است. همچنین ما با استفاده...

Asymptotic theory for stationary processes

In the study of random processes, dependence is the rule rather than the exception. To facilitate the related statistical analysis, it is necessary to quantify the dependence between observations. In the talk I will briefly review the history of this fundamental problem. By interpreting random processes as physical systems, I will introduce physical and predictive dependence coefficients that q...

Asymptotic Inference of Autocovariances of Stationary Processes

Abstract: The paper presents a systematic theory for asymptotic inference of autocovariances of stationary processes. We consider nonparametric tests for serial correlations based on the maximum (or L∞) and the quadratic (or L2) deviations. For these two cases, with proper centering and rescaling, the asymptotic distributions of the deviations are Gumbel and Gaussian, respectively. To establish...