The Laguerre process and generalized Hartman--Watson law

N ov 2 00 6 LAGUERRE PROCESS AND GENERALIZED HARTMAN - WATSON LAW

In this paper, we study complex Wishart processes or the so-called Laguerre processes (Xt) t≥0. We are interested in the behaviour of the eigenvalue process, we derive some useful stochastic differential equations and compute both the infinitesimal generator and the semi-group. We also give absolute-continuity relations between different indices. Finally, we compute the density function of the ...

The Operational matrices with respect to generalized Laguerre polynomials and their applications in solving linear dierential equations with variable coecients

In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...

Comparison between Rational Gegenbauer and Modified Generalized Laguerre Functions Collocation Methods for Solving the Case of Heat Transfer Equations Arising in Porous Medium

Numerical solution of Fredholm integral-differential equations on unbounded domain

In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...

Controlling Nonlinear Processes, using Laguerre Functions Based Adaptive Model Predictive Control (AMPC) Algorithm

Laguerre function has many advantages such as good approximation capability for different systems, low computational complexity and the facility of on-line parameter identification. Therefore, it is widely adopted for complex industrial process control. In this work, Laguerre function based adaptive model predictive control algorithm (AMPC) was implemented to control continuous stirred tank rea...