اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConstructing processes with prescribed mixing coefficients
62
0
0.0
(
0
)
تأليف
Leonid Kontorovich
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The rate at which dependencies between future and past observations decay in a random process may be quantified in terms of mixing coefficients. The latter in turn appear in strong laws of large numbers and concentration of measure results for dependent random variables. Questions regarding what rates are possible for various notions of mixing have been posed since the 1960s, and have important implications for some open problems in the theory of strong mixing conditions. This paper deals with $eta$-mixing, a notion defined in [Kontorovich and Ramanan], which is closely related to $phi$-mixing. We show that there exist measures on finite sequences with essentially arbitrary $eta$-mixing coefficients, as well as processes with arbitrarily slow mixing rates.
قيم البحث
اقرأ أيضاً
We present a method for constructing optimized equations for the modular curve X_1(N) using a local search algorithm on a suitably defined graph of birationally equivalent plane curves. We then apply these equations over a finite field F_q to efficie
ntly generate elliptic curves with nontrivial N-torsion by searching for affine points on X_1(N)(F_q), and we give a fast method for generating curves with (or without) a point of order 4N using X_1(2N).
Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do, are usually solved by reduction to the generalized Sturm--Liouville theory for differential operators. This inc
ludes the Brownian motion and a whole class of processes, which derive from it by means of linear transformations. The more general eigenproblem for the {em fractional} Brownian motion (f.B.m.) is not solvable in closed form, but the exact asymptotics of its eigenvalues and eigenfunctions can be obtained, using a method based on analytic properties of the Laplace transform. In this paper we consider two processes closely related to the f.B.m.: the fractional Ornstein--Uhlenbeck process and the integrated fractional Brownian motion. While both derive from the f.B.m. by simple linear transformations, the corresponding eigenproblems turn out to be much more complex and their asymptotic structure exhibits new effects.
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that appear in
the limit are random, typically non--Gaussian and belong to a Wiener chaos. They can be interpreted as wavelet coefficients of a generalized self-similar process.
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the constraint set
comprises the set of all equimeasurable rearrangements of a given function (representing vorticity) that have prescribed impulse (lnear momentum). A form of orbital stability is deduced.
We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by equivalent
classes of polynomials with prescribed coefficients. Simplified expressions are derived for some special cases. Our results extend some earlier results.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
