This paper presents an approximate formula for pricing average options when the underlying asset price is driven by time-changed Lévy processes. Time-changed Lévy processes are attractive to use for a driving factor of underlying prices because the processes provide a flexible framework for...

With continually increasing data sizes, the relevance of the big n problem of classical likelihood approaches is greater than ever. The functional mixed-effects model is a well established class of models for analyzing functional data. Spatial functional data in a mixed-effects setting is...

This paper proposes a spatial functional formulation of the normal mixed effect model for the statistical classification of spatially dependent Gaussian curves, in both parametric and state space model frameworks. Fixed effect parameters are represented in terms of a functional multiple...

Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic integration requires specific developments. Multifractional...

We define a covariance-type operator on Wiener space: for F and G two random variables in the Gross–Sobolev space D1,2 of random variables with a square-integrable Malliavin derivative, we let ΓF,G≔〈DF,−DL−1G〉, where D is the Malliavin derivative operator and L−1 is the...

In this paper, we consider a class of nonlocal stochastic Kuramoto–Sivashinsky equations driven by additive noises. Under some appropriate conditions, we investigate long time behavior, i.e., stability and growth bounds of the solutions to the equation. Finally, several examples are given to...