Fredholm representation of multi-parameter Gaussian processes with applications to equivalence in law and series expansions
Sottinen, Tommi; Viitasaari, Lauri (2015)
Sottinen, Tommi
Viitasaari, Lauri
VTeX
2015
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2021041510511
https://urn.fi/URN:NBN:fi-fe2021041510511
Kuvaus
vertaisarvioitu
© 2015 The Author(s). Published by VTeX. Open access article under the CC BY license.
© 2015 The Author(s). Published by VTeX. Open access article under the CC BY license.
Tiivistelmä
We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm kernel.
Kokoelmat
- Artikkelit [2573]