Related papers: Generalized covariation for Banach space valued pr…

Consider a uniform variate on the unit upper-half sphere of dimension $d$. It is known that the straight-line projection through the center of the unit sphere onto the plane above it distributes this variate according to a $d$-dimensional…

We consider estimating the shared mean of a sequence of heavy-tailed random variables taking values in a Banach space. In particular, we revisit and extend a simple truncation-based mean estimator first proposed by Catoni and Giulini. While…

This is an attempt to build Banach space valued theory for certain singular integrals on Hamming cube. Of course all estimates below are dimension independent, and we tried to find ultimate sharp assumptions on the Banach space for a…

We present several constructions of paths and processes with finite quadratic variation along a refining sequence of partitions, extending previous constructions to the non-uniform case. We study in particular the dependence of quadratic…

Non-Archimedean analogs of Markov quasimeasures and stochastic processes are investigated. Thery are used for the development of stochastic antiderivations. The non-Archimedean analog of the It$\hat o$ formula is proved.

The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of…

This paper considers the class of stochastic processes $X$ which are Volterra convolutions of a martingale $M$. When $M$ is Brownian motion, $X$ is Gaussian, and the class includes fractional Brownian motion and other Gaussian processes…

In this paper we introduce a variant of Burkholder's martingale transform associated with two martingales with respect to different filtrations. Even though the classical martingale techniques cannot be applied, we show that the discussed…

In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…

We prove an integral representation result for variational functionals in the space $BV^{\mathcal{B}}$ of functions with bounded $\mathcal{B}$-variation where $\mathcal{B}$ denotes a $k$-th order, $\mathbb{C}$-elliptic, linear homogeneous…

In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach is based on the idea of variational inequalities,…

The paper aims at developing the Bayesian seasonally cointegrated model for quarterly data. We propose the prior structure, derive the set of full conditional posterior distributions, and propose the sampling scheme. The identification of…

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous It\^o semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent…

We present a new approach to define a suitable integral for functions with values in quasi-Banach spaces. The integrals of Bochner and Riemann have deficiencies in the non-locally convex setting. The study of an integral for $p$-Banach…

In this paper the notion of an abstract square function (estimate) is introduced as an operator X to gamma (H; Y), where X, Y are Banach spaces, H is a Hilbert space, and gamma(H; Y) is the space of gamma-radonifying operators. By the…

A continuous quadratic form ("quadratic form", in short) on a Banach space $X$ is: (a) delta-semidefinite (i.e., representable as a difference of two nonnegative quadratic forms) if and only if the corresponding symmetric linear operator…

This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate It\^o semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and…

We consider the application of the generalized Convolution Quadrature (gCQ) to approximate the solution of an important class of sectorial problems. The gCQ is a generalization of Lubich's Convolution Quadrature (CQ) that allows for…

Representations of polynomial covariance type commutation relations are constructed on Banach spaces $L_p$ and $C[\alpha, \beta],\ \alpha,\beta\in \mathbb{R}$. Representations involve operators with piecewise functions, multiplication…

Brownian motions, martingales, and Wiener processes are introduced and studied for set valued functions taking values in the subfamily of compact convex subsets of arbitrary Banach space $X$. The present paper is an application of one the…