Related papers: Numerical schemes for radial Dunkl processes
For a star-shaped Kac-Moody root system, we provide an effective algorithm to obtain representatives of the Weyl group orbits of roots with a given norm and implement it as a computer program. We also explain the relationship between these…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions $d\geq 1$. Examples include Gaussian processes, in particular, fractional Brownian motions with Hurst index $H\in…
In this paper, we establish the theory of chaos propagation and propose an Euler-Maruyama scheme for McKean-Vlasov stochastic differential equations driven by fractional Brownian motion with Hurst exponent $H \in (0,1)$. Meanwhile, upper…
In this paper, we study an approximation scheme for L\'evy processes with drift in terms of a representation that is akin to the celebrated Mehler formula for L\'evy-Ornstein-Uhlenbeck processes. The approximation scheme is based on a…
In geostatistical problems with massive sample size, Gaussian processes can be approximated using sparse directed acyclic graphs to achieve scalable $O(n)$ computational complexity. In these models, data at each location are typically…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional…
We propose a discretization of the optimality principle in dynamic programming based on radial basis functions and Shepard's moving least squares approximation method. We prove convergence of the approximate optimal value function to the…
We study Bessel and Dunkl processes $(X_{t,k})_{t\ge0}$ on $\mathbb R^N$ with possibly multivariate coupling constants $k\ge0$. These processes describe interacting particle systems of Calogero-Moser-Sutherland type with $N$ particles. For…
We describe an exact simulation algorithm for the increments of Brownian motion on a sphere of arbitrary dimension, based on the skew-product decomposition of the process with respect to the standard geodesic distance. The radial process is…
We write down the generalized Bessel function associated with the root system of type $D$ by means of multivariate hypergeometric series. Our hint comes from the particular case of the Brownian motion in the Weyl chamber of type $D$.
We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending…
Let $f = \sum_{k=0}^n \varepsilon_k z^k$ be a random polynomial, where $\varepsilon_0,\ldots ,\varepsilon_n$ are iid standard Gaussian random variables, and let $\zeta_1,\ldots,\zeta_n$ denote the roots of $f$. We show that the point…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…
In this paper, we investigate the optimal strong convergence rate of numerical approximations for the Cox--Ingersoll--Ross model driven by fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. To deal with the difficulties caused…
We will introduce Euler-Maruyama approximations given by an orthogonal system in $L^{2}[0,1]$ for high dimensional SDEs, which could be finite dimensional approximations of SPDEs. In general, the higher the dimension is, the more one needs…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
By using a symbolic technique known in the literature as the classical umbral calculus, we characterize two classes of polynomials related to L\'evy processes: the Kailath-Segall and the time-space harmonic polynomials. We provide the…