Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
Normal martingales and polynomial families
Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve...
Note on the selection properties of set-valued semimartingales
Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
Note sur l'exposé précédent
Nouveaux résultats sur le grossissement des tribus
On a conjecture of Kazamaki
On a Martingale Related to a Strictly Stationary Random Process in R1.
On a non symmetric operation for two-parameter martingales
On an identity in law obtained by A. Földes and P. Révész
On asymptotic behaviour of local martingales
On certain probabilities equivalent to coin-tossing, d'après Schachermayer
On continuous conditional gaussian martingales and stable convergence in law
On convergence and regularity of two-parameter (Δ1) submartingales
On convergence of semimartingales
On ℝd-valued peacocks
In this paper, we consider ℝd-valued integrable processes which are increasing in the convex order, i.e. ℝd-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝd-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝd-valued martingale. This extends former results, obtained notably by Strassen [Ann. Math. Stat. 36 (1965) 423–439], Doob [J. Funct. Anal. 2 (1968) 207–225] and Kellerer [Math. Ann. 198 (1972) 99–122].
On equivalent martingale measures with bounded densities
On Existence of Local Martingale Measures for Insiders who Can Stop at Honest Times
We consider a market with two types of agents with different levels of information. In addition to a regular agent, there is an insider whose additional knowledge consists of being able to stop at an honest time Λ. We show, using the multiplicative decomposition of the Azéma supermartingale, that if the martingale part of the price process has the predictable representation property and Λ satisfies some mild assumptions, then there is no equivalent local martingale measure for the insider. This...
On extremal solutions of martingale problems
On filtrations related to purely discontinuous martingales
On independent times and positions for Brownian motions.