Related papers: On conditional expectations of finite index

This study is about the Iterated Function System (IFS) of similarities on $\mathbb R$ that satisfies Weak Separation property (WSP). We explore if this implies Finite type property. We look into the most simple case with condition that…

The single-index model is a statistical model for intrinsic regression where responses are assumed to depend on a single yet unknown linear combination of the predictors, allowing to express the regression function as $ \mathbb{E} [ Y | X ]…

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot...\cdot(n_lg)$ where $g\in G$ and $n_1,\cdots,n_l\in[1,{\hbox{\rm ord}}(g)]$, and the index $\ind(S)$ of $S$ is defined to be the…

The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…

In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a…

We study unitary orthonormal bases in the sense of Pimsner and Popa for inclusions $(\mathcal{B}\subseteq \mathcal{A}, E),$ where $\mathcal{A}, \mathcal{B}$ are finite dimensional von Neumann algebras and $E$ is a conditional expectation…

We prove a probabilistic generalization of the classic result that infinite power towers, $c^{c^{\dots}}$, converge if and only if $c\in[e^{-e},e^{1/e}]$. Given an i.i.d. sequence $\{A_i\}_{i\in\mathbb N}$, we find that convergence of the…

We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the…

Let $\mathcal{W}$ be the set of strongly real elements of $W$, a Coxeter group. Then for $w \in \mathcal{W}$, $e(w)$, the excess of $w$, is defined by $e(w) = \min\{\ell(x) + \ell(y) - \ell(w) \; | \; w=xy, x^2 = y^2 = 1\}$. When $W$ is…

We give sufficent conditions for a derivation of a $k$-algebra $A$ of finite type to be $\infty$-integrable in the sense of Hasse-Schmidt, when $A$ is a complete intersection, or when $A$ is reduced and $k$ is a regular ring. As a…

We formulate and prove a version of the Segal Conjecture for infinite groups. For finite groups it reduces to the original version. The condition that G is finite is replaced in our setting by the assumption that there exists a finite model…

Let $S=(a_1)\cdots(a_k)$ be a minimal zero-sum sequence over a finite cyclic group $G$. The index conjecture states that if $k=4$ and $\gcd(|G|,6)=1$, then $S$ has index 1. In this note we study the index conjecture and connect it to a…

Given an n-tuple {a_1, ..., a_n} of self-adjoint operators on an infinite dimensional Hilbert space H and a positive integer k, there exists a projection p of rank k such that, for each for j = 1, ..., n, pa_jp is a scalar multiple of p.…

The classical multidimensional version of Fatou's lemma (Schmeidler 1970) originally obtained for unconditional expectations and the standard non-negative cone in a finite-dimensional linear space is extended to conditional expectations and…

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

Let $X$ be a finitely generated left module over a left artinian ring $R$, and let $p(X)=\{l_i\}$ be the infinite sequence of nonnegative integers where $l_i$ is the length of the $i$-th term of the minimal projective resolution of $X$. We…

For a connected graph $G$, an instance $I$ is a set of pairs of vertices and a corresponding routing $R$ is a set of paths specified for all vertex-pairs in $I$. Let $\mathfrak{R}_I$ be the collection of all routings with respect to $I$.…

We consider a slightly modified form of the standard Rudin-Keisler order on ideals and demonstrate the existence of complete (with respect to this order) ideals in various projective classes. Using our methods, we obtain a simple proof of…

We examine situations, where representations of a finite-dimensional $F$-algebra $A$ defined over a separable extension field $K/F$, have a unique minimal field of definition. Here the base field $F$ is assumed to be a $C_1$-field. In…

We derive two forms of conditional a posteriori error estimates for a finite volume scheme approximating the parabolic-elliptic Keller-Segel system. The estimates control the error in the $L^\infty(0,T, L^2(\Omega))$- and…