Identifications optimales de paramètres pour un système linéaire excité par un bruit gaussien
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F. Brodeau (1983)
Annales de l'I.H.P. Probabilités et statistiques
Maurice Koskas (1977)
Séminaire de probabilités de Strasbourg
A. Bensoussan, J.-L. Lions (1977)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Myriam Fradon, Sylvie Rœlly (2007)
ESAIM: Probability and Statistics
We consider an infinite system of hard balls in undergoing Brownian motions and submitted to a smooth pair potential. It is modelized by an infinite-dimensional stochastic differential equation with an infinite-dimensional local time term. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also show that Gibbs measures are reversible measures.
Freddy Delbaen (1992)
Séminaire de probabilités de Strasbourg
James R. Norris (1988)
Séminaire de probabilités de Strasbourg
Svetlana Janković (1998)
Zbornik Radova
I. Stojkovic, O. van Gaans (2011)
Annales de l'I.H.P. Probabilités et statistiques
We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.
van Gaans, Onno, van Neerven, Jan (2006)
Electronic Communications in Probability [electronic only]
Katarzyna Horbacz (2002)
Annales Polonici Mathematici
We consider the stochastic differential equation (1) for t ≥ 0 with the initial condition u(0) = x₀. We give sufficient conditions for the existence of an invariant measure for the semigroup corresponding to (1). We show that the existence of an invariant measure for a Markov operator P corresponding to the change of measures from jump to jump implies the existence of an invariant measure for the semigroup describing the evolution of measures along trajectories and vice versa.
Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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