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The explicit Laplace transform for the Wishart process
Affine processes Wishart process ODE Laplace Transform
2011/7/19
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru (1991). We compare our methodology with the alter...
The explicit Laplace transform for the Wishart process
Affine processes Wishart process ODE Laplace Transform
2011/10/8
Abstract: We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the al...
A diffusion equation for the density of the ratio of Gaussian variables and the numerical inversion of Laplace transform
parabolic equations random matrices kernel estimation
2011/3/21
It is shown that the density of the ratio of two Gaussian random variables with the same variance satisfies a non stationary diffusion equation. Implications of this result for kernel density estimati...
Fractional Derivatives and Integrals on Time Scales via the Inverse Generalized Laplace Transform
fractional derivatives and integrals time scales Laplace transform
2011/1/19
We introduce a fractional calculus on time scales using the theory of delta (or nabla)dynamic equations. The basic notions of fractional order integral and fractional order derivative on an arbitrary ...
Multipliers of Laplace Transform Type for Laguerre and Hermite Expansions
Laguerre expansions Hermite expansions harmonic oscillator
2010/12/6
We present a new criterion for the boundedness in weighted Lp spaces of multiplier operators for Laguerre and Hermite expansions that arise from a Laplace-Stieltjes transform. As a special case, we re...
Laplace transform analysis of a multiplicative asset transfer model
wealth distribution master equation Laplace transform Boltzmann entropy
2010/10/20
We analyze a simple asset transfer model in which the transfer amount is a fixed fraction $f$ of the giver's wealth. The model is analyzed in a new way by Laplace transforming the master equation, sol...
Positive-part moments via the Fourier-Laplace transform
positive-part moments characteristic functions Fourier transforms Fourier-Laplace transforms integral representations
2010/3/18
Integral expressions for positive-part moments EXp
+ (p > 0) of random variables X are presented, in terms of the Fourier-Laplace or
Fourier transforms of the distribution of X. A necessary and suff...
Formulas for the Laplace Transform of Stopping Times based on Drawdowns and Drawups
Laplace Transform Drawdowns and Drawups
2010/11/3
In this work we study drawdowns and drawups of general diffu-sion processes. The drawdown process is defined as the current drop of the process from its running maximum, while the drawup process is de...
Computer-Aided Numerical Inversion of Laplace Transform
Laplace transform invariant networks linear system
2010/12/9
This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probabi...