10 citations · 22 across the 5 of their papers we have counts for
5 papers
A new integral equation for the first passage time density of the Ornstein-Uhlenbeck process
Dirk Veestraeten
The Laplace transform of the first passage time density of the Ornstein--Uhlenbeck process for a constant threshold contains a ratio of two parabolic cylinder functions for which n…
Some Laplace transforms and integral representations for parabolic cylinder functions and error functions
Dirk Veestraeten
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments…
Integral representations for products of two parabolic cylinder functions with different arguments and orders
Dirk Veestraeten
This paper derives new integral representations for products of two parabolic cylinder functions. In particular, expressions are obtained for D_{nu}(x)D_{mu}(y), with x>0 and y>0,…
Some integral representations and limits for (products of) the parabolic cylinder function
Dirk Veestraeten
Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the para…
On the inverse transform of Laplace transforms that contain (products of) the parabolic cylinder function
Dirk Veestraeten
The Laplace transforms of the transition probability density and distribution functions for the Ornstein-Uhlenbeck process contain the product of two parabolic cylinder functions,…