Related papers: A generalization of the rational rough Heston appr…

The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…

The strong-form asymmetric kernel-based collocation method, commonly referred to as the Kansa method, is easy to implement and hence is widely used for solving engineering problems and partial differential equations despite the lack of…

Let $( X ,d ,p ) $ be the pointed Gromov-Hausdorff limit of a sequence of pointed complete polarized K\"ahler manifolds $( M_l ,\omega_l ,\mathcal{L}_l ,h_l ,p_l ) $ with $Ric ( h_l ) =2\pi \omega_l $, $Ric ( \omega_l ) \geq -\Lambda…

In this work, we present a comprehensive framework for approximating the weakly singular power-law kernel $t^{\alpha-1}$ of fractional integral and differential operators, where $\alpha \in (0,1)$ and $t \in [\delta,T]$ with…

We consider linear approximation based on function evaluations in reproducing kernel Hilbert spaces of certain analytic weighted power series kernels and stationary kernels on the interval $[-1,1]$. Both classes contain the popular Gaussian…

We modify ETAS models by replacing the Pareto-like kernel proposed by Ogata with a Mittag-Leffler type kernel. Provided that the kernel decays as a power law with exponent $\beta + 1 \in (1,2]$, this replacement has the advantage that the…

For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first…

Learning with Fredholm kernel has attracted increasing attention recently since it can effectively utilize the data information to improve the prediction performance. Despite rapid progress on theoretical and experimental evaluations, its…

In this paper, we discuss the more general Hessian inequality $\sigma_{k}^{\frac{1}{k}}(\lambda (D_i (A\left(|Du|\right) D_j u)))\geq f(u)$ including the Laplacian, p-Laplacian, mean curvature, Hessian, k-mean curvature operators, and…

This paper deals with the \emph{integral} version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the H\"older regularity of the data. By…

For a complex number $x$, $\Vert x\Vert:=\min\{|x-m|:m\in\mathbb{Z}\}$. Let $k\geq 1$ be an integer, and $K$ be a number field. Let $\alpha_1,\ldots,\alpha_k$ be algebraic numbers with $|\alpha_i|\geq 1$ and let $d_i$ denotes the degree of…

In this article, we study the passage of limits from discrete to continuous condensing aggregation equation which comprises of Oort-Hulst-Safronov (OHS) equation together with inverse aggregation process. We establish the relation between…

An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel $|K_{(i\tau+\alpha)/2}(x)|^2, \alpha \ge 0,\ x…

We define $\lambda(r)$-convergence, which is a generalization of nontangential convergence in the unit disc. We prove Fatou-type theorems on almost everywhere nontangential convergence of Poisson-Stiltjes integrals for general kernels…

The exact solution in the LTB model with $f^2 = 1$, $\Lambda \ne 0$ is studied. The initial conditions for the metrical function and its derivatives generate the solution with complicated structure including the solutions like "stripping of…

Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm for a broad class of high-dimensional, path-dependent hedging…

We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…

The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…

We analyse the hard edge limit of the Muttalib-Borodin ensembles with general potential, and show that the limiting correlation kernel found in the ensemble with linear potential is universal. We also prove the Plancherel-Rotach type…

Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor…