Related papers: A hunt for sharp $L ^p$-estimates and rank-one con…
Full-history recursive multilevel Picard (MLP) approximation schemes have been shown to overcome the curse of dimensionality in the numerical approximation of high-dimensional semilinear partial differential equations (PDEs) with general…
In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equations in $L^p$ $(p\geq 1)$. We first study the existence and uniqueness for $L^p$ $(p>1)$ solutions by the method of…
One of the difficulties encountered when studying physical theories in discrete space-time is that of describing the underlying continuous symmetries (like Lorentz, or Galilei invariance). One of the ways of addressing this difficulty is to…
In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the…
In this short note, we will strengthen the classic Doob's $L^p$ inequality for sub-martingale processes. Because this inequality is of fundamental importance to the theory of stochastic process, we believe this generalization will find many…
We consider the problem of computing the q->p norm of a matrix A, which is defined for p,q \ge 1, as |A|_{q->p} = max_{x !=0 } |Ax|_p / |x|_q. This is in general a non-convex optimization problem, and is a natural generalization of the…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
In this paper, we determine the sharp \((p,q)\) range for \(L^p\)--\(L^q\) bounds of convolution operators \(f\mapsto \mu*f\) associated with fractal measures \(\mu\in \mathcal P_{\alpha,\beta}(\mathbb R^d)\), namely, compactly supported…
The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…
We establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, we…
The goal of this work is to study the existence and properties of non constant entire curves f drawn in a complex irreducible n-dimensional variety X, and more specifically to show that they must satisfy certain global algebraic or…
We prove an estimate for weighted $p$-th moments of the pathwise $r$-variation of a martingale in terms of the $A_{p}$ characteristic of the weight. The novelty of the proof is that we avoid real interpolation techniques.
We prove sharp $L^p(w)$ norm inequalities for the intrinsic square function (introduced recently by M. Wilson) in terms of the $A_p$ characteristic of $w$ for all $1<p<\infty$. This implies the same sharp inequalities for the classical…
The aim of this work is to obtain discrete versions of stochastic Gronwall inequalities involving demimartingale sequences. The results generalize the respective theorems for martingales provided by Kruse and Scheutzow (2018) and Hendy et…
Firstly we establish a sharp pointwise estimate for the arbitrary derivative of the function $f\in F_{\alpha}^{p},$ where $F_{\alpha}^{p}$ denotes the Fock space for $1\leq p<\infty.$ Then, in a particular Hilbert case when $p=2$ we…
We analyze the \textit{Large Deviation Probability (LDP)} of linear factor models generated from non-identically distributed components with \textit{regularly-varying} tails, a large subclass of heavy tailed distributions. An efficient…
We prove pointwise variational Lp bounds for a bilinear Fourier integral operator in a large but not necessarily sharp range of exponents. This result is a joint strengthening of the corresponding bounds for the classical Carleson operator,…
We present a new approach to noncommutative stochastic calculus that is, like the classical theory, based primarily on the martingale property. Using this approach, we introduce a general theory of stochastic integration and quadratic…
The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the H\"older spaces $H_p^{r,\alpha}$ for all $0<p\le\infty$ and $0<\alpha\le r$. By using modifications of the classical moduli of…
In this paper, we prove $L^p$ decay estimates for multilinear oscillatory integrals in $\mathbb{R}^2$, establishing sharpness through a scaling argument. The result in this paper is a generalization of the previous work by Gressman and Xiao…