In the framework of the theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, introduced by De Donno and Pratelli as a mathematical background to the theory of bond markets, we analyze a special class of integrands that preserve some nice properties of the finite-dimensional stochastic integral. In particular, we focus our attention on the class of processes considered by Mikulevicius and Rozovskii for the case of a locally square integrable cylindrical martingale and which includes an appropriate set of measure-valued processes.
De Donno, M., On a class of generalized integrands, <<STOCHASTIC ANALYSIS AND APPLICATIONS>>, 2007; 25 (6): 1167-1188. [doi:10.1080/07362990701567272] [http://hdl.handle.net/10807/168914]
On a class of generalized integrands
De Donno, Marzia
2007
Abstract
In the framework of the theory of stochastic integration with respect to a family of semimartingales depending on a continuous parameter, introduced by De Donno and Pratelli as a mathematical background to the theory of bond markets, we analyze a special class of integrands that preserve some nice properties of the finite-dimensional stochastic integral. In particular, we focus our attention on the class of processes considered by Mikulevicius and Rozovskii for the case of a locally square integrable cylindrical martingale and which includes an appropriate set of measure-valued processes.
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