Randomness and differentiability

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

Randomness and Differentiability

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) We show that a real number z ∈ [0, 1] is computably random if and only if every nondecreasing computable function [0, 1] → R is differentiable at z. (2) A real number z ∈ [0, 1] is weakly 2-random if and only if every almost everywhere differentiable computable function [0, 1] → R is diff...

متن کامل

Randomness and Differentiability (long Version)

We characterize some major algorithmic randomness notions via differentiability of effective functions. (1) As the main result we show that a real number z ∈ [0, 1] is computably random if and only if each nondecreasing computable function [0, 1] → R is differentiable at z. (2) We prove that a real number z ∈ [0, 1] is weakly 2-random if and only if each almost everywhere differentiable computa...

متن کامل

Fréchet directional differentiability and Fréchet differentiability

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

متن کامل

Effective genericity and differentiability

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x . This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions. 2010 Mathematics Subject Classification 03E15; 03F60 (p...

متن کامل

Efficiency and Hadamard Differentiability

Suppose an estimator sequence Tn. is asymptotically efficient for a. • smooth functional 1'1;. Then a Hadamard differentia.ble functional rf> applied to Tn is efficient for i f> 0 11':. More generally, Hadamard dif-ferentiability ma.y be used to esta.blish asymptotic efficiency. Three non-trivial applications are discussed: random right censoring, random truncation and estima.ting a. point symm...

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: Transactions of the American Mathematical Society

سال: 2015

ISSN: 0002-9947,1088-6850

DOI: 10.1090/tran/6484