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Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model

Florian Fuchs, Robert Stelzer (2013)

ESAIM: Probability and Statistics

We consider strictly stationary infinitely divisible processes and first extend the mixing conditions given in Maruyama [Theory Probab. Appl. 15 (1970) 1–22] and Rosiński and Żak [Stoc. Proc. Appl. 61 (1996) 277–288] from the univariate to the d-dimensional case. Thereafter, we show that multivariate Lévy-driven mixed moving average processes satisfy these conditions and hence a wide range of well-known processes such as superpositions of Ornstein − Uhlenbeck (supOU) processes or (fractionally integrated)...

On approach regions for the conjugate Poisson integral and singular integrals

S. Ferrando, R. Jones, K. Reinhold (1996)

Studia Mathematica

Let ũ denote the conjugate Poisson integral of a function f L p ( ) . We give conditions on a region Ω so that l i m ( v , ε ) ( 0 , 0 ) ( v , ε ) Ω ũ ( x + v , ε ) = H f ( x ) , the Hilbert transform of f at x, for a.e. x. We also consider more general Calderón-Zygmund singular integrals and give conditions on a set Ω so that s u p ( v , r ) Ω | ʃ | t | > r k ( x + v - t ) f ( t ) d t | is a bounded operator on L p , 1 < p < ∞, and is weak (1,1).

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