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Estimation and prediction in high dimensional multivariate factor stochastic volatility models is an important and active research area because such models allow a parsimonious representation of multivariate stochastic volatility. Bayesian…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
Within the context of the binomial model, we analyse sequences of values that are almost-uniform and we discuss a prediction method called the frequent outcome approach, in which the outcome that has occurred the most in the observed trials…
In statistics and machine learning, logistic regression is a widely-used supervised learning technique primarily employed for binary classification tasks. When the number of observations greatly exceeds the number of predictor variables, we…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…
We present a method for approximating solutions of Stochastic Differential Equations (SDEs) with arbitrary rates. This approximation is derived for bounded and measurable test functions. Specifically, we demonstrate that, leveraging the…
Let $(B(t))_{t\in \Theta}$ with $\Theta={\mathbb Z}$ or $\Theta={\mathbb R}$ be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in…
This paper studies a novel approach for approximating the behavior of compartmental spreading processes. In contrast to prior work, the methods developed describe a dynamics which bound the exact moment dynamics, without explicitly…
We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…
In this paper, we show an approximation in law of the complex Brownian motion by processes constructed from a stochastic process with independent increments. We give sufficient conditions for the characteristic function of the process with…
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…
We present analytical investigations of a multiplicative stochastic process that models a simple investor dynamics in a random environment. The dynamics of the investor's budget, $x(t)$, depends on the stochasticity of the return on…
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a…
We consider the problem of approximation of density functions which is important in the theory of pricing of basket options. Our method is well adopted to the multidimensional case. Observe that implementations of polynomial and spline…
This paper is devoted to the numerical analysis of a fully discrete finite element approximation for the stochastic Benjamin-Bona-Mahony equation driven by multiplicative noise. We first establish the existence and uniqueness of solutions…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
This paper considers the approximation of the continuous time filtering equation for the case of a multiple timescale (slow-intermediate, and fast scales) that may have correlation between the slow-intermediate process and the observation…
In this paper, we prove a Donsker type approximation theorem for the Rosenblatt process, which is a selfsimilar stochastic process exhibiting long range dependence. By using numerical results and simulated data, we show that this…
In this paper, we construct a class of stochastic interpolation neural network operators (SINNOs) with random coefficients activated by sigmoidal functions. We establish their boundedness, interpolation accuracy, and approximation…