Related papers: Direct Inversion for the Squared Bessel Process an…
New formulas for the moments about zero of the Non-central Chi-Squared and the Non-central Beta distributions are achieved by means of novel approaches. The mixture representation of the former model and a new expansion of the ascending…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
In this paper, we study the Schr\"odinger Bridge Problem (SBP), which is central to entropic optimal transport. For general reference processes and begin--endpoint distributions, we propose a forward-reverse iterative Monte Carlo procedure…
A number of problems in probability and statistics can be addressed using the multivariate normal (Gaussian) distribution. In the one-dimensional case, computing the probability for a given mean and variance simply requires the evaluation…
Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions…
A convenient way to represent a nonlinear input-output system in control theory is via a Chen-Fliess functional expansion or Fliess operator. The general goal of this paper is to describe how to approximate Fliess operators with iterated…
In this paper, we consider a stochastic model based on the Cox- Ingersoll- Ross model (CIR). The stochastic model is parameterized analytically by applying It\^o's calculus and the trend functions of the proposed process is calculated. The…
We consider a class of non-conjugate priors as a mixing family of distributions for a parameter (e.g., Poisson or gamma rate, inverse scale or precision of an inverse-gamma, inverse variance of a normal distribution) of an exponential…
A simple but successful strategy for building a discrete diffusion operator in finite volume schemes of industrial use is to correct the standard two-point flux approximation with a term accounting for the local mesh non-orthogonality.…
This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
The distributions of work for strongly non-equilibrium processes are studied using a very general form of a large-deviation approach, which allows one to study distributions of almost arbitrary quantities of interest for equilibrium,…
We present and analyze rigorously a quadratically convergent algorithm to compute an invariant circle for 2-dimensional maps along with the corresponding foliation by stable manifolds. We prove that when the algorithm starts from an initial…
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square root of the CIR process. We utilize the fact that…
We propose a determinant-free approach for simulation-based Bayesian inference in high-dimensional Gaussian models. We introduce auxiliary variables with covariance equal to the inverse covariance of the model. The joint probability of the…
We describe a Markov chain Monte Carlo method to approximately simulate a centered d-dimensional Gaussian vector X with given covariance matrix. The standard Monte Carlo method is based on the Cholesky decomposition, which takes cubic time…
We estimate the parameter of a stationary time series process by minimizing the integrated weighted mean squared error between the empirical and simulated characteristic function, when the true characteristic functions cannot be explicitly…
The discrete cosine transform is a valuable tool in analysis of data on undirected rectangular grids, like images. In this paper it is shown how one can define an analogue of the discrete cosine transform on triangles. This is done by…
We consider an integral transform given by $T_{\nu} f(s) := \pi \int_0^\infty rs J_{\nu}(r s)^2 f(r) \, dr$, where $J_{\nu}$ denotes the Bessel function of the first kind of order $\nu$. As shown by Walther (2002,…
We introduce a new paradigm for scaling simulations with projected entangled-pair states (PEPS) for critical strongly-correlated systems, allowing for reliable extrapolations of PEPS data with relatively small bond dimensions $D$. The key…