Deduction of Wold Representation of Stationary Processes from Cramer Representation of Second-Order Processes

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Spectral Representation of Stationary Processes

The spectral distribution measures the fraction of the total variance of the process γ(0) that can be attributed to a certain interval of frequencies.. If for example we have monthly data then one month corresponds to 2π, two month correspond to π, one year corresponds to π/6 . To measure the fraction of the variance generated by cyclical components of more than one year cycle length we would c...

متن کامل

Representation of Stooiastic Processes of Second Order and Linear Qperaticjjs

Series representations are obtained for the entire class of measurable, second order stochastic processes defined on any interval of the real line. They include as particular cases all earlier representations; they suggest a notion of "smoothness" that generalizes well known continuity notions; and they decompose the stochastic process into two orthogonal parts, the smooth part and a strongly d...

متن کامل

Karhunen-Loeve Representation of Periodic Second-Order Autoregressive Processes

In dynamic data driven applications modeling accurately the uncertainty of various inputs is a key step of the process. In this paper, we first review the basics of the Karhunen-Loève decomposition as a means for representing stochastic inputs. Then, we derive explicit expressions of one-dimensional covariance kernels associated with periodic spatial second-order autoregressive processes. We al...

متن کامل

Second Order Properties of Locally Stationary Processes

In this paper we investigate an optimal property of the maximum likelihood estimator of Gaussian locally stationary processes by the second order approximation. In the case where the model is correctly specified, it is shown that appropriate modifications of the maximum likelihood estimator for Gaussian locally stationary processes is second order asymptotically efficient. We discuss second ord...

متن کامل

State Space representation of non-stationary Gaussian Processes

The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where n is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS representation of the most important kernels used in machine learning. The aim ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The Annals of Probability

سال: 1975

ISSN: 0091-1798

DOI: 10.1214/aop/1176996360