I. Yaroslavtsev

collaborators

6 papers

math.PR2019

Local characteristics and tangency of vector-valued martingales

Ivan S. Yaroslavtsev

This paper is devoted to tangent martingales in Banach spaces. We provide the definition of tangency through local characteristics, basic $L^{p}$ - and $ϕ$ -estimates, a precise constr…

math.PR2018

On strongly orthogonal martingales in UMD Banach spaces

Ivan Yaroslavtsev

In the present paper we introduce the notion of strongly orthogonal martingales. Moreover, we show that for any UMD Banach space $X$ and for any $X$ -valued strongly orthogonal mart…

math.FA2018

The UMD property for Musielak--Orlicz spaces

Nick Lindemulder, Mark Veraar, Ivan Yaroslavtsev

In this paper we show that Musielak--Orlicz spaces are UMD spaces under the so-called $Δ_{2}$ condition on the generalized Young function and its complemented function. We also prove…

math.PR2018

Burkholder-Davis-Gundy inequalities in UMD Banach spaces

Ivan S. Yaroslavtsev

In this paper we prove Burkholder-Davis-Gundy inequalities for a general martingale $M$ with values in a UMD Banach space $X$ . Assuming that $M_{0} = 0$ , we show that the following two…

math.FA2018

The Hilbert transform and orthogonal martingales in Banach spaces

Adam Osękowski, Ivan Yaroslavtsev

Let $X$ be a given Banach space and let $M$ , $N$ be two orthogonal $X$ -valued local martingales such that $N$ is weakly differentially subordinate to $M$ . The paper contains the pr…

math.PR2018

Pointwise properties of martingales with values in Banach function spaces

Mark Veraar, Ivan Yaroslavtsev

In this paper we consider local martingales with values in a UMD Banach function space. We prove that such martingales have a version which is a martingale field. Moreover, a new B…