
Minimax rates for the covariance estimation of multidimensional Lévy processes with highfrequency data
This article studies nonparametric methods to estimate the cointegrated...
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Simulation of conditional expectations under fast meanreverting stochastic volatility models
In this short paper, we study the simulation of a large system of stocha...
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Maximal inequalities for stochastic convolutions and pathwise uniform convergence of time discretisation schemes
We prove a new BurkholderRosenthal type inequality for discretetime pr...
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A Hilbert Space of Stationary Ergodic Processes
Identifying meaningful signal buried in noise is a problem of interest a...
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Where are the Natural Numbers in Hilbert's Foundations of Geometry?
Hilbert's Foundations of Geometry was perhaps one of the most influentia...
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Volatility and intensity
When studying models and estimators in the setting of highfrequency dat...
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A note on quadratic forms of stationary functional time series under mild conditions
We study the distributional properties of a quadratic form of a stationa...
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A weak law of large numbers for realised covariation in a Hilbert space setting
This article generalises the concept of realised covariation to Hilbertspacevalued stochastic processes. More precisely, based on highfrequency functional data, we construct an estimator of the traceclass operatorvalued integrated volatility process arising in general mild solutions of Hilbert spacevalued stochastic evolution equations in the sense of Da Prato and Zabczyk (2014). We prove a weak law of large numbers for this estimator, where the convergence is uniform on compacts in probability with respect to the HilbertSchmidt norm. In addition, we show that the conditions on the volatility process are valid for most common stochastic volatility models in Hilbert spaces.
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