We survey some of the recent developments on quasi-Monte Carlo (QMC) methods, which,
in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main …

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein
distance Page 1 Bernoulli 25(4A), 2019, 2620–2648 https://doi.org/10.3150/18-BEJ1065 Sharp …

Due to the rapidly increasing need for methods of data compression, quantization has
become a flourishing field in signal and image processing and information theory. The same …

A new grid method for computing the Snell envelope of a function of an $\mathbb {R}^ d $-
valued simulatable Markov chain $(X_k) _ {0\lambda\leq k\lambda\leq n} $ is proposed.(This …

In this article, we study the approximation of a probability measure μ on Rd by its empirical
measure ˆμN interpreted as a random quantization. As error criterion we consider an …

This book is an extended written version of the Master 2 course “Probabilités
Numériques”(ie, Numerical Probability or Numerical Methods in Probability) which has been …

We present here the quantization method which is well‐adapted for the pricing and hedging
of American options on a basket of assets. Its purpose is to compute a large number of …

Optimal quantization has been recently revisited in multi-dimensional numerical integration
(see [18]), multi-asset American option pricing (see [2]), control theory (see [19]) and …

We review optimal quantization methods for numerically solving nonlinear problems in
higher dimensions associated with Markov processes. Quantization of a Markov process …

This work presents an empirical analysis of popular scenario generation methods for
stochastic optimization, including quasi-Monte Carlo, moment matching, and methods based …