Higher-order pathwise theory of fluctuations in stochastic homogenization

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

Scaling Limit of Fluctuations in Stochastic Homogenization

We investigate the global fluctuations of solutions to elliptic equations with random coefficients in the discrete setting. In dimension d ⩾ 3 and for i.i.d. coefficients, we show that after a suitable scaling, these fluctuations converge to a Gaussian field that locally resembles a (generalized) Gaussian free field. The paper begins with a heuristic derivation of the result, which can be read ...

متن کامل

Quantitative theory in stochastic homogenization

This course relies on a work in preparation with A. Gloria [2], which is a continuum version of [1]. It slightly differs from [2] because the present analysis does not rely on Green’s functions and treats the periodic case. For related work on an emerging quantitative theory of stochastic homogenization, including many references, we refer to three preprints, which are available on my web page:...

متن کامل

Higher-order Director Fluctuations

Standard theories of the influence of a fluctuating director on spin relaxation in nematic liquid crystals are based on the notion that the mean-square angular displacement (8’) of the director is small, such that terms of this and higher orders are negligible. One consequence of this ‘small-angle’ approximation is that director fluctuations contribute only to the spectral density J , ( o o ) a...

متن کامل

A Central Limit Theorem for Fluctuations in 1d Stochastic Homogenization

In this paper, we analyze the random fluctuations in a 1D stochastic homogenization problem and prove a central limit theorem: the first order fluctuations is described by a Gaussian process that solves an SPDE with an additive spatial white noise. Using a probabilistic approach, we obtain a precise error decomposition up to the first order, which also helps to decompose the limiting Gaussian p...

متن کامل

Pathwise Construction of Stochastic Integrals

We propose a method to construct the stochastic integral simultaneously under a non-dominated family of probability measures. Pathby-path, and without referring to a probability measure, we construct a sequence of Lebesgue-Stieltjes integrals whose medial limit coincides with the usual stochastic integral under essentially any probability measure such that the integrator is a semimartingale. Th...

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: Stochastics and Partial Differential Equations: Analysis and Computations

سال: 2019

ISSN: 2194-0401,2194-041X

DOI: 10.1007/s40072-019-00156-4