Stochastic Analysis of Gaussian Processes via Fredholm Representation | Zendy

Tommi Sottinen | Zendy; Lauri Viitasaari | Zendy

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Stochastic Analysis of Gaussian Processes via Fredholm Representation

Author(s) -

Tommi Sottinen,

Lauri Viitasaari

Publication year - 2016

Publication title -

international journal of stochastic analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.19

H-Index - 28

eISSN - 2090-3340

pISSN - 2090-3332

DOI - 10.1155/2016/8694365

Subject(s) - mathematics , fredholm determinant , fredholm theory , representation (politics) , fredholm integral equation , stochastic differential equation , equivalence (formal languages) , integrable system , brownian motion , gaussian , martingale representation theorem , separable space , stochastic process , mathematical analysis , pure mathematics , diffusion process , geometric brownian motion , integral equation , statistics , law , computer science , knowledge management , physics , innovation diffusion , quantum mechanics , politics , political science

We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. We show the convenience of the Fredholm representation by giving applications to equivalence in law, bridges, series expansions, stochastic differential equations, and maximum likelihood estimations

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