Displaying similar documents to “Spherical analysis on harmonic A N groups”

L-estimates for the wave equation on the Heisenberg group.

Detlef Müller, Elias M. Stein (1999)

Revista Matemática Iberoamericana

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Let £ denote the sub-Laplacian on the Heisenberg group H. We prove that e / (1 - £) extends to a bounded operator on L(H), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.

Concentration of the Brownian bridge on Cartan-Hadamard manifolds with pinched negative sectional curvature

Marc Arnaudon, Thomas Simon (2005)

Annales de l’institut Fourier

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We study the rate of concentration of a Brownian bridge in time one around the corresponding geodesical segment on a Cartan-Hadamard manifold with pinched negative sectional curvature, when the distance between the two extremities tends to infinity. This improves on previous results by A. Eberle, and one of us . Along the way, we derive a new asymptotic estimate for the logarithmic derivative of the heat kernel on such manifolds, in bounded time and with one...

Harmonic analysis in value at risk calculations.

Claudio Albanese, Luis Seco (2001)

Revista Matemática Iberoamericana

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Value at Risk is a measure of risk exposure of a portfolio and is defined as the maximum possible loss in a certain time frame, typically 1-20 days, and within a certain confidence, typically 95%. Full valuation of a portfolio under a large number of scenarios is a lengthy process. To speed it up, one can make use of the total delta vector and the total gamma matrix of a portfolio and compute a Gaussian integral over a region bounded by a quadric. We use methods from harmonic analysis...