Department of Economics and Business Economics

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

Research output: Research - peer-reviewJournal article

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
Volume124
Issue number5
Pages (from-to)1942-1973
ISSN0304-4149
DOIs
StatePublished - 2014

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