Les semi-martingales et la théorie de la mesure
Les semi-martingales formelles
Les systèmes simples sont disjoints de ceux qui sont infiniment divisibles et plongeables dans un flot
We prove that simple transformations are disjoint from those which are infinitely divisible and embeddable in a flow. This is a reinforcement of a previous result of A. del Junco and M. Lemańczyk [1] who showed that simple transformations are disjoint from Gaussian processes.
Les temps de passage successifs de l'intégrale du mouvement brownien
Les travaux d'Azéma sur le retournement du temps
L'estimation du spectre de processus de droites
Level crossings and other level functionals of stationary Gaussian processes.
Level crossings of a random polynomial with hyperbolic elements.
Level sets of multiparameter Brownian motions.
Level sets of random fields and applications: specular points and wave crests.
Levels at which every brownian excursion is exceptional
Lévy classes and self-normalization.
Lévy copulae for financial returns
The paper uses Lévy processes and bivariate Lévy copulae in order to model the behavior of intraday log-returns. Based on assumptions about the form of marginal tail integrals and a Clayton Lévy copula, the model allows for capturing intraday cross-dependency. The model is applied to VaR of the portfolios constructed on stock returns as well as on cryptocurrencies. The proposed method shows fair performance compared to classical time series models.
Lévy processes conditioned on having a large height process
In the present work, we consider spectrally positive Lévy processes not drifting to and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with ) before hitting . This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law of this conditioned process (starting at ) is defined as a Doob -transform via a martingale. For Lévy processes with infinite variation paths, this martingale...
Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group
Lévy Processes, Saltatory Foraging, and Superdiffusion
It is well established that resource variability generated by spatial patchiness and turbulence is an important influence on the growth and recruitment of planktonic fish larvae. Empirical data show fractal-like prey distributions, and simulations indicate that scale-invariant foraging strategies may be optimal. Here we show how larval growth and recruitment in a turbulent environment can be formulated as a hitting time problem for a jump-diffusion process. We present two theoretical results. Firstly,...
Lévy processes that can creep downwards never increase
Lévy's area under conditioning
L'exponentielle stochastique des groupes de Lie
L'Hospital type rules for monotonicity: Applications to probability inequalities for sums of bounded random variables.