On the equivalence of multiparameter Gaussian processes

DOI10.1007/s10959-006-0022-5zbMath1127.60031OpenAlexW2117395112MaRDI QIDQ867078

Ciprian A. Tudor, Tommi Sottinen

Publication date: 14 February 2007

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-006-0022-5

zbMATH Keywords

stochastic differential equationsGirsanov theoremHitsuda representationcanonical representation of Gaussian processesequivalence of Gaussian processesShepp representation

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic integrals (60H05) Continuity and singularity of induced measures (60G30)

Related Items (10)

Spectral conditions for equivalence of Gaussian random fields with stationary increments ⋮ The 1-d stochastic wave equation driven by a fractional Brownian sheet ⋮ Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions ⋮ When is a linear combination of independent fBm's equivalent to a single fBm? ⋮ Stability results for stochastic differential equations driven by an additive fractional Brownian sheet ⋮ Parameter estimation for stochastic equations with additive fractional Brownian sheet ⋮ Long-range dependent completely correlated mixed fractional Brownian motion ⋮ Stochastic differential equations driven by an additive fractional Brownian sheet ⋮ Generalized Gaussian bridges ⋮ Transfer principle for $n$th order fractional Brownian motion with applications to prediction and equivalence in law

Cites Work

• Non-anticipative representations of equivalent Gaussian processes
• Multiple stochastic fractional integrals: A transfer principle for multiple stochastic fractional integrals
• Integration questions related to fractional Brownian motion
• Are classes of deterministic integrands for fractional Brownian motion on an interval complete?
• Itô formula and local time for the fractional {B}rownian sheet
• On Gaussian processes equivalent in law to fractional Brownian motion
• Representation of Gaussian processes equivalent to Wiener process
• Equivalence of Volterra processes.
• Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
• Radon-Nikodym Derivatives of Gaussian Measures
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