We derive conditional Edgeworth-type expansions for Skorohod and Itô integrals with respect to Brownian motion, based on cumulant operators defined by the Malliavin calculus. As a consequence we obtain conditional Stein approximation bounds for multiple stochastic integrals and quadratic Brownian functionals.

We present a generalization of Hilfer derivatives in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties. Further, we show some applications of these generalized Hilfer–Prabhakar derivatives in classical equations of mathematical physics, like the heat and the free electron laser equations, and in difference-differential equa...

Case-cohort design, an outcome-dependent sampling design for censored survival data, is increasingly used in biomedical research. The development of asymptotic theory for a case-cohort design in the current literature primarily relies on counting process stochastic integrals. Such an approach, however, is rather limited and lacks theoretical justification for outcome-dependent weighted methods ...

Abstract We study via the chaotic calculus the independence of multiple stochastic integrals In(fn), Im(gm) with respect to martingales (Mt)t∈IR+ that satisfy a deterministic structure equation. It is shown that if the integrals are independent and if a contraction denoted as fn ◦1 gm does not vanish on A ∈ B(IR+), a.e., then the stochastic measure associated to (Mt)t∈IR+ is Gaussian on A. In t...

We derive sampleepaths continuity results for some sto-chastic Volterra integrals with degenerate kernel under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. Embeddings of Besov spaces into sets of HHlder continuous functions are the key elements. RRSUMM. Nous montrons la continuitt trajectorielle d...

This text describes several methods to approximate multivariate integrals. Cubature formulae that are exact for a space of polyno-mials and Monte Carlo methods are the best known. More recently developed methods such as quasi-Monte Carlo methods (including lattice rules), Smolyak rules and stochastic integration rules are also described. This short note describes the contents of a session keyno...