Related papers: Continuous-time sparse domination
Distributional identities for a L\'evy process $X_t$, its quadratic variation process $V_t$ and its maximal jump processes, are derived, and used to make "small time" (as $t\downarrow0$) asymptotic comparisons between them. The…
This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H\"{o}rmander conditions. As applications, we obtain the strong type quantitative weighted…
We address second-order optimality conditions for optimal control problems involving sparsity functionals which induce spatio-temporal sparsity patterns. We employ the notion of (weak) second subderivatives. With this approach, we are able…
When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
For a Dawson-Watanabe superprocess $X$ on $\mathbb{R}^d$, it is shown in Perkins (1990) that if the underlying spatial motion belongs to a certain class of L\'evy processes that admit jumps, then with probability one the closed support of…
We prove a sparse bound in the context of Schauder theory for divergence form elliptic partial differential equations. In addition, we show how an iteration argument inspired by sparse domination bounds can be used to deduce gradient…
Defining a divergence between the laws of continuous martingales is a delicate task, owing to the fact that these laws tend to be singular to each other. An important idea, put forward by N. Gantert, is to instead consider a scaling limit…
From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…
The problem of sparse approximation and the closely related compressed sensing have received tremendous attention in the past decade. Primarily studied from the viewpoint of applied harmonic analysis and signal processing, there have been…
Consider a discrete-time martingale, and let $V^2$ be its normalized quadratic variation. As $V^2$ approaches 1, and provided that some Lindeberg condition is satisfied, the distribution of the rescaled martingale approaches the Gaussian…
We prove a sparse bound for the $m$-sublinear form associated to vector-valued maximal functions of Fefferman-Stein type. As a consequence, we show that the sparse bounds of multisublinear operators are preserved via $\ell^r$-valued…
In this paper we study maximal $L^p$-regularity for evolution equations with time-dependent operators $A$. We merely assume a measurable dependence on time. In the first part of the paper we present a new sufficient condition for the…
The concept of a L\'evy subordinator is generalized to a family of non-decreasing stochastic processes, which are parameterized in terms of two Bernstein functions. Whereas the independent increments property is only maintained in the…
We prove that the best so far known constant $c_p=\frac{p^{-p}}{1-p},\, p\in(0,1)$ of a domination inequality, which originates to Lenglart, is sharp. In particular, we solve an open question posed by Revuz and Yor. Motivated by the…
We use the principle of almost orthogonality to give a new and simple proof that a sparse Lerner operator is bounded on a matrix- or operator-weighted space $L_W^{2}(\mu)$, where $\mu$ is a doubling measure on $\R^d$ if and only if the…
The $L^p$ maximal inequalities for martingales are one of the classical results in the theory of stochastic processes. Here we establish the sharp moderate maximal inequalities for one-dimensional diffusion processes, which include the…
Instance sparsification is well-known in the world of exact computation since it is very closely linked to the Exponential Time Hypothesis. In this paper, we extend the concept of sparsification in order to capture subexponential time…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition…