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Minimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data
This article studies nonparametric methods to estimate the co-integrated...
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Simulation of conditional expectations under fast mean-reverting 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 Burkholder-Rosenthal type inequality for discrete-time 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 high-frequency 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 Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated volatility process arising in general mild solutions of Hilbert space-valued 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 Hilbert-Schmidt 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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