On the stability of stationary solutions of a linear integro-differential equation.
Periodic in distribution solution for a telegraph equation.
Phase transition and Martin boundary
Points, lignes et systèmes d'arrêt flous et problème d'arrêt optimal
Processus gaussiens, markoviens d'ordre p, fortement markoviens d'ordre p et problème de Dirichlet stochastique
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.
Quelques Proprietes sur le Produit Tensoriel des Distributions Stochastiques du Schwartz
Risk bounds for new M-estimation problems
In this paper, we consider a new framework where two types of data are available: experimental data Y1,...,Yn supposed to be i.i.d from Y and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon Y. We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data n, reduced model complexity and computing budget m. The method we present is general enough to cover a wide range of applications....
Selections of set-valued stochastic processes.
Semigroups associated with generalized Brownian functional.
Semimartingales à deux indices
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...
Small ball probabilities for stable convolutions
We investigate the small deviations under various norms for stable processes defined by the convolution of a smooth function with a real SαS Lévy process. We show that the small ball exponent is uniquely determined by the norm and by the behaviour of f at zero, which extends the results of Lifshits and Simon, Ann. Inst. H. Poincaré Probab. Statist.41 (2005) 725–752 where this was proved for f being a power function (Riemann-Liouville processes). In the Gaussian case, the same generality as...
Spectral type of a polynomial of stationary Gaussian process
Stationäre zufällige Punktfolgen. II.*)
Stochastic Differential Equations Driven by Generalized Positive Noise
Stochastic integration on nuclear spaces and its applications
Stochastic processes associated with thermal quasi-free states
Sur la transformée de Fourier de H. H. Kuo
Sur un travail de R. Carmona et D. Nualart