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.
On the occupation measure of super-Brownian motion.
On the Structure of Spatial Branching Processes
The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching...
On two fragmentation schemes with algebraic splitting probability
Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with and respectively, for some a > 0. In the first (resp. second) case, since smaller...
Optimal transportation for multifractal random measures and applications
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is intuitively some kind of multistep transportation. Applications are given for construction of multifractal random changes of times and to the existence of random metrics, the volume forms of which coincide with the multifractal random measures.