Hermite martingales
Hiding a constant drift
The following question is due to Marc Yor: Let B be a brownian motion and St=t+Bt. Can we define an -predictable process H such that the resulting stochastic integral (H⋅S) is a brownian motion (without drift) in its own filtration, i.e. an -brownian motion? In this paper we show that by dropping the requirement of -predictability of H we can give a positive answer to this question. In other words, we are able to show that there is a weak solution to Yor’s question. The original question, i.e.,...
Hilbert-valued anticipating stochastic differential equations
How the maximum of gaussian random walks and fields is influenced by changes of the variances.
In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.
Hsu-Robbins and Spitzer's theorems for the variations of fractional Brownian motion.
Hyperdefinite stochastic integration I: The nonstandard theory.
Hyperdefinite stochastic integration II: Comparision with the standard theory.
Hyperdefinite stochastic integration III: Hyperdefinite representations of standard martingales.
Incompleteness of the bond market with Lévy noise under the physical measure
The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.
Indefinite quadratic functionals of gaussian processes and least-action paths
Inégalités de normes pour les intégrales stochastiques
Inégalités isopérimétriques et calcul stochastique
Integral representation of martingales in the brownian excursion filtration
Intégrale multiple de Stratonovich pour le processus de Poisson
Intégrale stochastique curviligne le long d'une courbe rectifiable
Intégrales stochastiques de processus anticipants et projections duales prévisibles.
We define a stochastic anticipating integral δμ with respect to Brownian motion, associated to a non adapted increasing process (μt), with dual projection t. The integral δμ(u) of an anticipating process (ut) satisfies: for every bounded predictable process ft,E [ (∫ fsdBs ) δμ(u) ] = E [ ∫ fsusdμs ].We characterize this integral when μt = supt ≤s ≤ 1 Bs. The proof relies on a path decomposition of Brownian motion up to time 1.
Intégrales stochastiques généralisées
Intégrales stochastiques non monotones
Intégrales stochastiques par rapport à une semi-martingale vectorielle et changements de filtration
Intégrales stochastiques par rapport au processus de Wiener à deux paramètres