Convergence of stochastic processes [Abstract of thesis]
Correction to the paper "Random functionals on K{M_{p}} spaces" (Studia Math., 39 (1971), pp. 233-240)
Deux remarques sur la séparabilité optionnelle
Distributive laws. Applications to stochastic automata. (Lois distributives. Applications aux automates stochastiques.)
Equivalence of Gaussian measures of finite sum of stochastic processes
Espaces probabilisés filtrés : de la théorie de Vershik au mouvement brownien, via des idées de Tsirelson
Estimation de moyennes et fonctions de répartition de suites d'échantillonnage
Example of continuous second-order stochastic process with prescribed finite multiplicity
Existence of nontrivial stochastic monoids.
Fonctions-spline et espérances conditionnelles de champs gaussiens
Génération d'une famille de tribus par un processus croissant
Generation of -fields by step processes
Grandes déviations et loi fonctionnelle du logarithme itéré pour les processus aléatoires
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.,...
Le théorème d'isomorphisme d'Ornstein et la classification des systèmes dynamiques en théorie ergodique
Modelling Real World Using Stochastic Processes and Filtration
First we give an implementation in Mizar [2] basic important definitions of stochastic finance, i.e. filtration ([9], pp. 183 and 185), adapted stochastic process ([9], p. 185) and predictable stochastic process ([6], p. 224). Second we give some concrete formalization and verification to real world examples. In article [8] we started to define random variables for a similar presentation to the book [6]. Here we continue this study. Next we define the stochastic process. For further definitions...
Neighbourhoods of independence and associated geometry in manifolds of bivariate Gaussian and Freund distributions
We provide explicit information geometric tubular neighbourhoods containing all bivariate distributions sufficiently close to the cases of independent Poisson or Gaussian processes. This is achieved via affine immersions of the 4-manifold of Freund bivariate distributions and of the 5-manifold of bivariate Gaussians. We provide also the α-geometry for both manifolds. The Central Limit Theorem makes our neighbourhoods of independence limiting cases for a wide range of bivariate distributions; the...
Non tangential convergence for the Ornstein-Uhlenbeck semigroup.
Non-anticipative Integral Transformations of Stochastic Processes
On The Decomposition Of Arbitrary Second Ordered Stochastic Process