Related papers: CLT for martingales-III: discontinuous compensator…
In this paper, employing the weak convergence method, based on a variational representation for expected values of positive functionals of a Brownian motion, we investigate moderate deviation %(CLT for abbreviation) for a class of…
In this paper we prove the existence of weak martingale solutions to the stochastic Navier-Stokes Equations driven by pure jump L\'evy processes. Our proof consists of two parts. In the first one, mostly classical, we recall a priori…
We provide martingale analogs of weakly cancelling differential operators and prove a Sobolev-type embedding theorem for these operators in the martingale setting.
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is…
The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…
In this paper we introduce the concept of conic martingales}. This class refers to stochastic processes having the martingale property, but that evolve within given (possibly time-dependent) boundaries. We first review some results about…
Many practical optimization problems lack strong convexity. Fortunately, recent studies have revealed that first-order algorithms also enjoy linear convergences under various weaker regularity conditions. While the relationship among…
The main objective consists in generalizing a well-known It{\^o} formula of J. Jacod and A. Shiryaev: given a c{\`a}dl{\`a}g process S, there is an equivalence between the fact that S is a semimartingale with given characteristics (B^k , C,…
We consider a strictly stationary and ergodic sequence of random elements taking values in some Hilbert space. Our target is to study the weak convergence of the discrete Fourier transforms under sharp conditions. As a side-result we obtain…
Using a martingale concentration inequality, concentration bounds `from time $n_0$ on' are derived for stochastic approximation algorithms with contractive maps and both martingale difference and Markov noises. These are applied to…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…
This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…
In the first part of this paper we give easy and intuitive proofs for the small value probabilities of the martingale limit of a supercritical Galton-Watson process in both the Schr\"oder and the B\"ottcher case. These results are…
In this paper, the weak convergence of impulsive recurrent process with Markov switching in the scheme of Levy approximation is proved. For the relative compactness, a method proposed by R. Liptser for semimartingales is used with a…
We obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums $S_n=\sum_{j=1}^{n}\xi_{j,n}$ of triangular arrays $\{\xi_{1,n},\xi_{2,n},...,\xi_{n,n}\}$ satisfying some mixing and…
This work deals with the asymptotic distribution of both potentials and couplings of entropic regularized optimal transport for compactly supported probabilities in $\R^d$. We first provide the central limit theorem of the Sinkhorn…
For moving average processes with random coefficients and heavy-tailed innovations that are weakly dependent in the sense of strong mixing and local dependence condition $D'$ we study joint functional convergence of partial sums and maxima.…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
We develop a general approach of the almost sure central limit theorem for the quasi-continuous vectorial martingales and we release a quadratic extension of this theorem while specifying speeds of convergence. As an application of this…
This work provides some general theorems about unconditional and conditional weak convergence of empirical processes in the case of Poisson sampling designs. The theorems presented in this work are stronger than previously published…