Closedness of some spaces of stochastic integrals
Convex analysis for sets of local martingales measures
Décompositions multiplicatives de semimartingales exponentielles et applications
En cherchant une caractérisation variationnelle des martingales
Exponential martingales and CIR model
With the use of exponential martingales and the Girsanov theorem we show how to calculate bond prices in a large variety of square root processes. We clarify and correct several errors that abound in financial literature concerning these processes. The most important topics are linear risk premia, the Longstaff double square model, and calculations concerning correlated CIR processes.
Extending Lévy's characterisation of brownian motion
Fonction maximale et variation quadratique des martingales en présence d'un poids
Fourier multipliers for non-symmetric Lévy processes
We study Fourier multipliers resulting from martingale transforms of general Lévy processes.
-spaces, p≤1, and spline systems
Homogénéisation pour des processus associés à des frontières perméables
Inégalité de Sobolev sur l'espace de Poisson
Isomorphismes entre espaces
Józef Marcinkiewicz: analysis and probability
We briefly review Marcinkiewicz's work, on analysis, on probability, and on the interplay between the two. Our emphasis is on the continuing vitality of Marcinkiewicz's work, as evidenced by its influence on the standard works. What is striking is how many of the themes that Marcinkiewicz studied (alone, or with Zygmund) are very much alive today. What this demonstrates is that Marcinkiewicz and Zygmund, as well as having extraordinary mathematical ability, also had excellent mathematical taste.
Local martingales measures
Martingale operators and Hardy spaces generated by them
Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the norm of the sharp operator is equivalent to the norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method....
Martingales browniennes et conjecture de Sakai
Martingales, G...-Embeddings and Quotients of L1 .
Maximum principle and comparison theorem for quasi-linear stochastic PDE's.
Monotonic rearrangements of functions with small mean oscillation
We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous" ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named α-extension.
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...