White noise based stochastic calculus associated with a class of Gaussian processes

2010/08/01 by Daniel Alpay, Alpay, Daniel, Haim Attia +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #46A12 #60G15 #60G22 #60H05 #60H40 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications #math.FA #math.PR #msc:46A12 #msc:60G15 #msc:60G22 #msc:60H05 #msc:60H40

paper · pdf · doi:10.48550/arxiv.1008.0186

arxiv created 2010/08/01 · openalex publication_date 2010/08/01 · arxiv updated 2010/08/03 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

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.

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