Related papers: Second order Riesz transforms on multiply-connecte…

We provide a systematic approach to twisting differential KO-theory leading to a construction of the corresponding twisted differential Atiyah-Hirzebruch spectral sequence (AHSS). We relate and contrast the degree two and the degree one…

The abstraction of the study of stochastic processes to Banach lattices and vector lattices has received much attention by Grobler, Kuo, Labuschagne, Stoica, Troitsky and Watson over the past fifteen years. By contrast mixing processes have…

Let $G = N \rtimes A$, where $N$ is a stratified group and $A = \mathbb{R}$ acts on $N$ via automorphic dilations. Homogeneous sub-Laplacians on $N$ and $A$ can be lifted to left-invariant operators on $G$ and their sum is a sub-Laplacian…

For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…

We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into…

In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…

One of the celebrated results by Riesz \cite{Rie} is the Riesz conjugate functions theorem for analytic functions in the complex plane $\mathbb{C}$. The study on the Riesz conjugate functions theorem for functions in higher dimensional…

Continuous limits of discrete systems with long-range interactions are considered. The map of discrete models into continuous medium models is defined. A wide class of long-range interactions that give the fractional equations in the…

Let $M$ be a complete non-compact Riemannian manifold satisfying the doubling volume property as well as a Gaussian upper bound for the corresponding heat kernel. We study the boundedness of the Riesz transform $d\Delta ^{-\frac{1}{2}}$ on…

In this paper, we study stochastic optimization of two-level composition of functions without Lipschitz continuous gradient. The smoothness property is generalized by the notion of relative smoothness which provokes the Bregman gradient…

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted…

In this paper, we investigate the numerical solution of the two-dimensional fractional Laplacian wave equations. After splitting out the Riesz fractional derivatives from the fractional Laplacian, we treat the Riesz fractional derivatives…

A natural counterpart to the Lie-Trotter product formula for norm-continuous one-parameter semigroups is proved, for the class of quasicontractive quantum stochastic operator cocycles whose expectation semigroup is norm continuous. Compared…

We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…

Construction of an united theory of the subdifferentials of the first and second orders is interesting for many specialists in optimization \cite{morduchrockafel}. In the paper the rules for construction of the subdifferentials of the first…

Optimization-based robot control strategies often rely on first-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly second-order partial derivatives of the…

In this article, we construct an It\^o integral with respect to a two-sided finite-variance L\'evy process $\{L(x)\}_{x\in \mathbb{R}}$, without a Gaussian component. Using Rosenthal inequality for discrete-time martingales, we give an…

We continue the study of the correlation functions for the point stochastic processes introduced in Part I (G.Olshanski, math.RT/9804086). We find an integral representation of all the correlation functions and their explicit expression in…

We give an extension of L\^e's stochastic sewing lemma [Electron. J. Probab. 25: 1 - 55, 2020]. The stochastic sewing lemma proves convergence in $L_m$ of Riemann type sums $\sum _{[s,t] \in \pi } A_{s,t}$ for an adapted two-parameter…

In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…