This paper studies a classical extension of the Black and Scholes model of option pricing, often known as the Hull and White model. Our specificity is that the volatility process is assumed not only to be stochastic, but also to have long memory features and properties. We study here the...

In this paper, we study the problem of non parametric estimation of the spectral density f of a stationary Gaussian sequence. For this purpose, we consider a collection of finite dimensional linear spaces (e.g. linear space spanned by wavelets or piecewise polynomials on possibly irregular grids...

We consider a model <italic>Y</italic>_null = σ_nullη_null in which (σ_null) is not independent of the noise process (η_null) but σ_null is independent of η_null for each <italic>t</italic>. We assume that (σ_null) is stationary, and we propose an adaptive estimator of the density of ln(σ_null²) based on the observations <italic>Y</italic>_null....