Boundary processes : the calculus of processes diffusing on the boundary
Bounded double square functions
We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For , we determine the sharp order of local integrability obtained when the square function of is in . The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of in .
Brownian Motion, Reflection Groups and Tanaka Formula
Brownian penalisations related to excursion lengths, VII
Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.
Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property....
Calculs stochastiques directs sur les trajectoires et propriétés des boréliens porteurs
Caractérisation des martingales à deux paramètres indépendantes du chemin
Caractérisation des semimartingales
Caractérisation des semimartingales, d'après Dellacherie
Caractérisation d'une classe de semimartingales
Caractérisation d’une classe d’ensembles convexes de ou
Caractéristiques locales des semi-martingales et changements de probabilités
Carthaginian enlargement of filtrations
This work is concerned with the theory of initial and progressive enlargements of a reference filtration F with a random timeτ. We provide, under an equivalence assumption, slightly stronger than the absolute continuity assumption of Jacod, alternative proofs to results concerning canonical decomposition of an F -martingale in the enlarged filtrations. Also, we address martingales’ characterization in the enlarged filtrations in terms of martingales in the reference filtration, as well as predictable...
Changing time for two-parameter strong martingales
Chaoticity on a stochastic interval
Characterization of a regular family of semimartingales by line integrals.
Classe et martingales fortes à paramètre bidimensionnel
Closed sets supporting a continuous divergent martingale
Comments on a single server queue.
Comparison principle approach to utility maximization
We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.