Related papers: Asymmetric Doob inequalities in continuous time

We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, the fractional integration operator is a martingale transform, however, it may vanish if the filtration is excessively…

In this paper we study minimax Aubry-Mather measures and its main properties. We consider first the discrete time problem and then the continuous time case. In the discrete time problem we establish existence, study some of the main…

We extend the well-known 't Hooft anomaly matching conditions for continuous global symmetries to discrete groups. We state the matching conditions for all possible anomalies which involve discrete symmetries explicitly. There are two types…

This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…

Inspired by the recent work [MRT21], we prove a non-universal non-central Moderate Deviation principle for the nodal length of arithmetic random waves (Gaussian Laplace eigenfunctions on the standard flat torus) both on the whole manifold…

In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for discrete-time matrix local martingales,…

Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…

In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic…

This is a revised version of the doctoral dissertation of the same title, written under the supervision of Professor Krzysztof Stempak in 2019. For general (possibly nondoubling) metric measure spaces various properties of the associated…

In this paper we obtain a martingale representation theorem in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ of the filtration $\mathbb{F}^L$ generated by a L\'evy process $L$. The assumptions on the random time are that…

We consider convergence properties of the long-term behaviors with respect to the coefficient of the stochastic term for a nonautonomous stochastic $p$-Laplacian lattice equation with multiplicative noise. First, the upper semi-continuity…

In this paper, we study the observability and controllability of wave equations coupled by first or zero order terms on a compact manifold. We adopt the approach in Dehman-Lebeau's paper \cite{DehmanLebeau09} to prove that: the weak…

We consider the Frank-Wolfe algorithm for solving variational inequalities over compact, convex sets under a monotone $C^1$ operator and vanishing, nonsummable step sizes. We introduce a continuous-time interpolation of the discrete…

Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace $\tau$. Let $d$ be an injective positive measurable operator with respect to $(\mathcal{M}, \tau)$ such that $d^{-1}$ is also measurable.…

We consider decoupling inequalities for random variables taking values in a Banach space $X$. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process can be…

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…

In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of continuous functions from time 0 to T. The underlying measure P is…

Let $f_1, f_2, ..., f_n$ be a family of independent copies of a given random variable f in a probability space $(\Omega, \mathcal{F}, \mu)$. Then, the following equivalence of norms holds whenever $1 \le q \le p < \infty$…

We analyse the performance of a recursive Monte Carlo method for the Bayesian estimation of the static parameters of a discrete--time state--space Markov model. The algorithm employs two layers of particle filters to approximate the…