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References in periodicals archive ?
The idea of the proof is to represent the Laplace transform of [[tau].sup.([??]).sub.r] as an integral with respect to the distribution of ([tau], [B.sub.[tau]]) by the Cameron-Martin formula, which is similar to the calculation used in [5].
The homotopy analysis transform method (Hatm) is a compounding of the homotopy analysis method (HAM) and Laplace transform method (Khan, Gondala, Hussain, & Vanani, 2012; Gondal, Arife, Khan, & Hussain, 2011; Kumar, Singh, & Kumar, 2014; Kumar, Kumar, & Baleanu, 2016).
The strength of the ARG process is that its dynamics can be easily characterized by the conditional Laplace transform:
Classical control theory uses the Laplace transform, a method to change differential equations in the time domain into a regular algebraic polynomial in the transform domain.
They write primarily for applied mathematicians who need to address the problems of inverting the Laplace transform of probability density (or of a positive function), but suggest that risk managers in banking and insurance should also be aware of the potential and effectiveness of the methodology for determining risk capital and the computation of premia.
This concept of improper fuzzy Riemann integral was later exploited by Allahviranloo and Ahmadi in [10] to introduce the fuzzy Laplace transform, which they used to solve some first-order fuzzy differential equations (FDEs).
The Laplace transform [phi](z) or L of a function f(t) is defined by [92]
The Laplace transform is an integral transform that is powerful and useful technique to solve differential equations, which transforms the original differential equation into an algebraic equation.
The Laplace transform methods for option pricing originate from the idea of randomizing the maturity in [1].
Now, we define the Laplace transform of a function f(x) of a variable x [member of] [R.sup.+] by
However, the authors will develop the necessary mathematical machinery employing the Laplace Transform inversion integral and contour integration of complex variable theory in order to analytically evaluate (5) and (6).