Moderate Deviations 13

نویسنده

  • A. DEMBO
چکیده

We prove that the Moderate Deviation Principle (MDP) holds for the trajectory of a locally square integrable martingale with bounded jumps as soon as its quadratic covariation, properly scaled, converges in probability at an exponential rate. A consequence of this MDP is the tightness of the method of bounded martingale diierences in the regime of moderate deviations.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Moderate and Large Deviations for Erdős-kac Theorem

as n → ∞. This is a deep extension of Hardy-Ramanujan Theorem (see [13]). In addition, the central limit theorem holds in a more general setting for additive functions. A formal treatment and proofs can be found in e.g. Durrett [7]. In terms of rate of convergence to the Gaussian distribution, i.e. Berry-Esseen bounds, Rényi and Turán [18] obtained the sharp rate of convergenceO(1/ √ log logn)....

متن کامل

Moderate deviations for random fields and random complex zeroes

Moderate deviations for random complex zeroes are deduced from a new theorem on moderate deviations for random fields.

متن کامل

Delta Method in Large Deviations and Moderate Deviations for Estimators by Fuqing

The delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics, while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities. The large and moderate deviation theory can achieve this goal. Motivated by the delta method in weak convergence, a general delta method in large devi...

متن کامل

Large and moderate deviations principles for recursive kernel estimators of a multivariate density and its partial derivatives

Abstract: In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic behaviour not only for the moderate deviations scale but also for the large deviations one. We provide results both for the pointwise and the unifor...

متن کامل

Moderate Deviations for System Identification: Error Bounds from a Probability Concentration Perspective

This paper is devoted to moderate deviations for characterizing parameter estimation errors in system identification. Moderate deviations for system identification provide probabilistic error bounds that are beyond laws of large numbers and central limit theorems, and cannot be expressed in terms of large deviations bounds. Such error bounds are crucial in complexity analysis for system identif...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996