Probabilistic interpretation of a system of semi-linear parabolic partial differential equations
Probability limit identification functions on separable metrizable spaces
Problème des martingales et équations différentielles stochastiques associées à un opérateur intégro-différentiel
Progrès récents en calcul stochastique quantique
Propagation of chaos and fluctuations for a moderate model with smooth initial data
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Propagation of Growth Uncertainty in a Physiologically Structured Population
In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent...
Properties of generalized set-valued stochastic integrals
The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...
Quadratic BSDEs with random terminal time and elliptic PDEs in infinite dimension.
Quantitative results for perturbed stochastic differential equations.
Quantum random walk revisited
In the framework of the symmetric Fock space over L²(ℝ₊), the details of the approximation of the four fundamental quantum stochastic increments by the four appropriate spin-matrices are studied. Then this result is used to prove the strong convergence of a quantum random walk as a map from an initial algebra 𝓐 into 𝓐 ⊗ ℬ (Fock(L²(ℝ₊))) to a *-homomorphic quantum stochastic flow.
Quantum stochastic differential equations driven by free noises and dilations of markovian semigroups
Quasi-diffusion solution of a stochastic differential equation
We consider the stochastic differential equation , where , , are nonrandom continuous functions of t, X₀ is an initial random variable, is a Gaussian process and X₀, Y are independent. We give the form of the solution () to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that () is a quasi-diffusion proces.
Quasistable gradient and Hamiltonian systems with a pairwise interaction randomly perturbed by Wiener processes.
Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct.
Quelques formules asymptotiques pour les petites perturbations de systèmes dynamiques
Quelques méthodes de résolution de problèmes de dynamique stochastique non linéaire
Quelques remarques sur un nouveau type d'équations différentielles stochastiques
Random and deterministic perturbations of nonlinear oscillators.
Random fixed points and random differential inclusions.