In order to prove the existence and the uniqueness of operator solutions of some white noise stochastic differential equations, we need some multidimensional non adapted estimates of white noise stochastic integrals on a dense domains in bosonic Fock space. These estimates are not sufficient to prove the fundamental unitary conditions. For this we need to introduce the adapteness and to restrict ourselves to 1-dimensional index set.
Accardi, L., Ayed, W., Ouerdiane, H. (2005). White noise approach to stochastic integration. RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 13(4), 369-398 [10.1515/156939705775992448].
White noise approach to stochastic integration
ACCARDI, LUIGI;
2005-01-01
Abstract
In order to prove the existence and the uniqueness of operator solutions of some white noise stochastic differential equations, we need some multidimensional non adapted estimates of white noise stochastic integrals on a dense domains in bosonic Fock space. These estimates are not sufficient to prove the fundamental unitary conditions. For this we need to introduce the adapteness and to restrict ourselves to 1-dimensional index set.File in questo prodotto:
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