Department of Economics and Business Economics

Limit theorems for power variations of ambit field driven by white noise

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

We study the asymptotics of lattice power variations of two-parameter ambit fields driven by white noise. Our first result is a law of large numbers for power variations. Under a constraint on the memory of the ambit field, normalized power variations converge to certain integral functionals of the volatility field associated to the ambit field, when the lattice spacing tends to zero. This result holds also for thinned power variations that are computed by only including increments that are separated by gaps with a particular asymptotic behavior. Our second result is a stable central limit theorem for thinned power variations.
Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)1942-1973
Publication statusPublished - 2014

See relations at Aarhus University Citationformats

ID: 68846148