Related papers: Central limit theorems for multilevel Monte Carlo …
The batch means estimator of the MCMC variance is a simple and effective measure of accuracy for MCMC based ergodic averages. Under various regularity conditions, the estimator has been shown to be consistent for the true variance. However,…
Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…
Markov chain Monte Carlo (MCMC) produces a correlated sample for estimating expectations with respect to a target distribution. A fundamental question is when should sampling stop so that we have good estimates of the desired quantities?…
We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…
In this paper, we introduce the $\sigma$-antithetic multilevel Monte Carlo (MLMC) estimator for a multi-dimensional diffusion which is an extended version of the original antithetic MLMC one introduced by Giles and Szpruch \cite{a}. Our aim…
We analyze the fluctuations of incomplete $U$-statistics over a triangular array of independent random variables. We give criteria for a Central Limit Theorem (CLT, for short) to hold in the sense that we prove that an appropriately scaled…
We formulate and prove a new sufficient conditions for Central Limit Theorem(CLT) in the space of continuous functions in the terms typical for the approximation theory. We prove that the conditions for continuous CLT obtained by N.C.Jain…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exponentially tempered L\'evy process. The algorithm, based on…
We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
In this paper, we present a generalisation of the Multilevel Monte Carlo (MLMC) method to a setting where the level parameter is a continuous variable. This Continuous Level Monte Carlo (CLMC) estimator provides a natural framework in PDE…
Sample covariance matrices are widely used in multivariate statistical analysis. The central limit theorems (CLT's) for linear spectral statistics of high-dimensional non-centered sample covariance matrices have received considerable…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\xi_j$, perturbed by predictable multiplicative factors $\lambda_j$ with values in intervals $[\underline\lambda_j,\overline\lambda_j]$. It…
We show that repulsive random variables can yield Monte Carlo methods with faster convergence rates than the typical $N^{-1/2}$, where $N$ is the number of integrand evaluations. More precisely, we propose stochastic numerical quadratures…
Conditional Monte Carlo (CMC) has been widely used for sensitivity estimation with discontinuous integrands as a standard simulation technique. A major limitation of using CMC in this context is that finding conditioning variables to ensure…
It is well known that Monte Carlo integration with variance reduction by means of control variates can be implemented by the ordinary least squares estimator for the intercept in a multiple linear regression model. A central limit theorem…
In this paper, we establish the convergence rate in central limit theorem (CLT) for linearly extended negative quadrant dependent (LENQD) random variables (rv's). Under some weak conditions, the rate of normal approximation is shown as…
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous…
This article considers the sequential Monte Carlo (SMC) approximation of ratios of normalizing constants associated to posterior distributions which in principle rely on continuum models. Therefore, the Monte Carlo estimation error and the…