6 Result(s)
within
Nizar Demni
Probability Theory and Stochastic Processes
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Article
Quaternionic Brownian Windings
We define and study the three-dimensional windings along Brownian paths in the quaternionic Euclidean, projective and hyperbolic spaces. In particular, the asymptotic laws of these windings are shown to be Gau...
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Article
The Horizontal Heat Kernel on the Quaternionic Anti-De Sitter Spaces and Related Twistor Spaces
The geometry of the quaternionic anti-de Sitter fibration is studied in details. As a consequence, we obtain formulas for the horizontal Laplacian and subelliptic heat kernel of the fibration. The heat kernel ...
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Article
Moments of the Hermitian Matrix Jacobi Process
In this paper, we compute the expectation of traces of powers of the Hermitian matrix Jacobi process for a large enough but fixed size. To proceed, we first derive the semi-group density of its eigenvalues pro...
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Chapter
Large Deviations for Clocks of Self-similar Processes
The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a Lévy process drifting to $$\in...
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Chapter
Spectral Distribution of the Free Unitary Brownian Motion: Another Approach
We revisit the description provided by Ph. Biane of the spectral measure of the free unitary Brownian motion. We actually construct for any $...
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Chapter
Radial Dunkl Processes Associated with Dihedral Systems
We are interested in radial Dunkl processes associated with dihedral systems. We write down the semi-group density and as a by-product the generalized Bessel function and the W-invariant generalized Hermite polyn...
