Fonctions aléatoires à valeurs dans certains espaces nucléaires. (Random functions with values in certain nuclear spaces)
Fonctions aléatoires à valeurs dans certains espaces nucléaires. (Random functions with values in certain nuclear spaces)
In the theory of stochastic processes the notion of separability plays an important role to get results on the regularity of the trajectories of a process. For a stochastic process (indexed by a separable metric space) with values in a Lusin space a general theorem on the existence of a separable modification is proved, and then used to obtain a result on the existence of continuous modifications. In a second part it is shown that the assumptions made in the general results are fulfilled in the case of some general classes of nuclear spaces. For the proofs a new variant of the Minlos inequality is used.
Probability measures on topological spaces, separable modification, Probability theory on linear topological spaces, Foundations of stochastic processes, nuclear spaces, Sample path properties, regularity of the trajectories, Minlos inequality
Probability measures on topological spaces, separable modification, Probability theory on linear topological spaces, Foundations of stochastic processes, nuclear spaces, Sample path properties, regularity of the trajectories, Minlos inequality