اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConvergence theorems for barycentric maps
65
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We first develop a theory of conditional expectations for random variables with values in a complete metric space $M$ equipped with a contractive barycentric map $beta$, and then give convergence theorems for martingales of $beta$-conditional expectations. We give the Birkhoff ergodic theorem for $beta$-values of ergodic empirical measures and provide a description of the ergodic limit function in terms of the $beta$-conditional expectation. Moreover, we prove the continuity property of the ergodic limit function by finding a complete metric between contractive barycentric maps on the Wasserstein space of Borel probability measures on $M$. Finally, the large derivation property of $beta$-values of i.i.d. empirical measures is obtained by applying the Sanov large deviation principle.
قيم البحث
اقرأ أيضاً
In this article we prove three fundamental types of limit theorems for the $q$-norm of random vectors chosen at random in an $ell_p^n$-ball in high dimensions. We obtain a central limit theorem, a moderate deviations as well as a large deviations pri
nciple when the underlying distribution of the random vectors belongs to a general class introduced by Barthe, Guedon, Mendelson, and Naor. It includes the normalized volume and the cone probability measure as well as projections of these measures as special cases. Two new applications to random and non-random projections of $ell_p^n$-balls to lower-dimensional subspaces are discussed as well. The text is a continuation of [Kabluchko, Prochno, Thale: High-dimensional limit theorems for random vectors in $ell_p^n$-balls, Commun. Contemp. Math. (2019)].
Under the sublinear expectation $mathbb{E}[cdot]:=sup_{thetain Theta} E_theta[cdot]$ for a given set of linear expectations ${E_theta: thetain Theta}$, we establish a new law of large numbers and a new central limit theorem with rate of convergence.
We present some interesting special cases and discuss a related statistical inference problem. We also give an approximation and a representation of the $G$-normal distribution, which was used as the limit in Peng (2007)s central limit theorem, in a probability space.
Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. Thi
s notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps.
The classic Fatou lemma states that the lower limit of a sequence of integrals of functions is greater or equal than the integral of the lower limit. It is known that Fatous lemma for a sequence of weakly converging measures states a weaker inequalit
y because the integral of the lower limit is replaced with the integral of the lower limit in two parameters, where the second parameter is the argument of the functions. This paper provides sufficient conditions when Fatous lemma holds in its classic form for a sequence of weakly converging measures. The functions can take both positive and negative values. The paper also provides similar results for sequences of setwise converging measures. It also provides Lebesgues and monotone convergence theorems for sequences of weakly and setwise converging measures. The obtained results are used to prove broad sufficient conditions for the validity of optimality equations for average-cost Markov decision processes.
We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space $R^n$, the hyperbolic space $H^n$ and a Riemannian manifold $mathfrak{S^n}$ ($ngeq 3$) with the Schwarzschild metric to any Riemannian manifold $N$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
