Parametric dependence of the solution processes on the coefficients in McShane's stochastic integral equation systems
Partition-dependent stochastic measures and -deformed cumulants.
Poisson stochastic integration in Hilbert spaces
Positivité sur l'espace de Fock
Power variation of multiple fractional integrals
Principal values of the integral functionals of brownian motion : existence continuity and an extension of Itô's formula
Probabilistic models for vortex filaments based on fractional brownian motion.
Se introduce una estructura de vorticidad basada en el movimiento browniano fraccionario con parámetro de Hurst H > 1/2 . El objeto de esta nota es presentar el siguiente resultado: Bajo una condición de integrabilidad adecuada sobre la medida ρ que controla la concentración de la vorticidad a lo largo de los filamentos, la energía cinética de la configuración está bien definida y tiene momentos de todos los órdenes.
Probabilistic models of vortex filaments
A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between and are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.
Probability structure preserving and absolute continuity
Problèmes de Dirichlet-Neumann étalés et fonctionnelles multiplicatives associées
Prolongement de processus holomorphes. Cas «carré intégrable»
Prolongement des semi-martingales
Properties of generalized set-valued stochastic integrals
The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...
Properties of set-valued stochastic integrals
We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.
Propriété des lois pour les solutions d'une famille d'équations stochastiques
Q-adapted quantum stochastic integrals and differentials in Fock scale
In this paper we first introduce the Fock-Guichardet formalism for the quantum stochastic (QS) integration, then the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures, on a space-time σ-field , of the QS integration. Then rigorous analysis of the QS integrals is carried out, and continuity of the QS derivative D is proved. Finally, Q-adapted dynamics is discussed, including Bosonic (Q = I), Fermionic (Q = -I), and monotone (Q = O) quantum...
Quantum stochastic calculus on full Fock space
We present a new version of integration of time-adapted processes with respect to creation, annihilation and conservation processes on the full Fock space. Among the new features, in the first place, there is a new formulation of adaptedness which is both simpler and more general than the known ones. The new adaptedness allows for processes which are not restricted to be elements of some norm closure of the ∗-algebra which is generated by the basic creation processes.
Quasimartingales et formes linéaires associées
Quasi-martingales et variations
Quelques cas de représentation chaotique