In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

In the paper, we propose two new efficient methods for pricing barrier option in wide classes of Lévy processes with/without regime switching. Both methods are based on the numerical Laplace transform inversion formulae and the Fast Wiener-Hopf factorization method developed in Kudryavtsev and Levendorskǐi (Finance Stoch. 13: 531–562, 2009). The first method uses the Gaver-Stehfest algorithm, t...

Keywords: Black–Scholes equation Completely monotonic function Finite difference scheme Laplace Transform M-Matrix Positivity-preserving Post–Widder formula a b s t r a c t In this paper we explore discrete monitored barrier options in the Black–Scholes framework. The discontinuity arising at each monitoring data requires a careful numerical method to avoid spurious oscillations when low volati...

In this paper, we introduce a q-analogue of the P-Widder transform and give a Parseval-Goldstein type theorem. Furthermore, we evaluate the q-Laplace transform of a product of q-Bessel functions. Several special cases of our results are also pointed out.

In this article, Stancu type Post-Widder operators are introduced, which a modification of the that preserve functions constant and e^2ax for fixed a>0. The uniform convergence these modified function f on [0,∞) is examined then rate investigated with help continuity module. Voronovskaja asymptotic formula obtained to examine behavior operators. Finally, numerical examples graphs given s...

Abstract We consider the Post–Widder operators of semi-exponential type, which are a generalization exponential connected with $$x^2$$ x 2 . This modification has beauty to find difference other operators, while original do not have such property. estimate quantitative ...

We present a characterization of the approximation errors of the Post-Widder and the Gamma operators in Lp[0, ∞), 1 ≤ p ≤ ∞, with a weight x γ for any real γ. Two types of characteristics are used – weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it.