Abstract Theory of random processes needs a kind of normal distribution. This is why
Gaussian vectors and Gaussian distributions in infinite-dimensional spaces come into play …

We consider the joint SPX-VIX calibration within a general class of Gaussian polynomial
volatility models in which the volatility of the SPX is assumed to be a polynomial function of a …

We study numerical integration of Lipschitz functionals on a Banach space by means of
deterministic and randomized (Monte Carlo) algorithms. This quadrature problem is shown …

Vector Quantization is the name given to discretization methods based on nearest
neighbour search. It was developed in the 1950s, mostly in signal processing and …

We investigate the connections between the mean pathwise regularity of stochastic
processes and their L r (ℙ)-functional quantization rates as random variables taking values …

In this chapter, we present an overview of the recent developments of vector quantization
and functional quantization and their applications as a numerical method in finance, with an …

We present a fully constructive method for quantization of the solution X of a scalar SDE in
the path space L p [0, 1] or C [0, 1]. The construction relies on a refinement strategy which …

Some general theoretical works on Gaussian measures are also included whenever they
treat inequalities widely used in small deviation theory. Also included are the relevant …

We present a survey of results on minimal errors and optimality of algorithms for strong and
weak approximation of systems of stochastic differential equations. For strong …

We survey recent results on numerical integration with respect to measures μ on infinite-
dimensional spaces, eg, Gaussian measures on function spaces or distributions of diffusion …