Mesures aléatoires localement finies
Mesures aléatoires -régulières
Mild solution of the heat equation with a general stochastic measure
The stochastic heat equation on [0,T]×ℝ driven by a general stochastic measure is investigated. Existence and uniqueness of the solution is established. Hölder regularity of the solution in time and space variables is proved.
Moments of stochastic processes governed by Poisson random measures
Multidimensional multifractal random measures.
Multiplicative chaos and random translation
Musielak-Orlicz spaces and prediction problems
By a harmonizable sequence of random variables we mean the sequence of Fourier coefficients of a random measure M: (n = 0,±1,...) The paper deals with prediction problems for sequences Xₙ(M) for isotropic and atomless random measures M. The crucial result asserts that the space of all complex-valued M-integrable functions on the unit interval is a Musielak-Orlicz space. Hence it follows that the problem for Xₙ(M) (n = 0,±1,...) to be deterministic is in fact an extremal problem of Szegö’s type...
Mutually catalytic branching in the plane : uniqueness
Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities
To filter perturbed local measurements on a random medium, a dynamic model jointly with an observation transfer equation are needed. Some media given by PDE could have a local probabilistic representation by a Lagrangian stochastic process with mean-field interactions. In this case, we define the acquisition process of locally homogeneous medium along a random path by a Lagrangian Markov process conditioned to be in a domain following the path and conditioned to the observations. The nonlinear...
Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion
On applications of Little's formula.
On intensities of modulated Cox measures.
On long time almost sure asymptotics of renormalized branching diffusion processes
On modulated random measures.
On random discrete distributions
On randomized stopping times.
In this note we give a proof of the fact that the extremal elements of the set of randomized stopping times are exactly the stopping times.
On the asymptotic behavior of the second moment of the Fourier transform of a random measure.
On the conditional intensity of a random measure
We prove the existence of the conditional intensity of a random measure that is absolutely continuous with respect to its mean; when there exists an L-intensity, , the conditional intensity is obtained at the same time almost surely and in the mean.
On the Construction of Random Measures
On the mode-change problem for random measures.