White noise based stochastic calculus associated with a class of Gaussian processes Academic Article uri icon

abstract

  • Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula. Subjects: Probability (math. PR); Functional Analysis (math. FA) MSC classes: 60H40, 60H05, 60G15, 60G22, 46A12 Cite as: arXiv: 1008.0186 [math. PR](or arXiv: 1008.0186 v1 [math. PR] for this version) Submission history From: Daniel Alpay A [view email][v1] Sun, 1 Aug 2010 16: 38: 42 GMT (17kb)

publication date

  • August 1, 2010