Laplace transform stochastic models

This transform is widely used to formulate semi-Markov stochastic models, where t and / (t) are the random variable and its probability density function, respectively. In Table F.l, we briefly report some Laplace transform pairs. 

Another stochastic model (4.27)-(4.32) treatment can be made tvhen the aim is to calculate the average time of residence and the axial dispersion coefficient. In this problem, we use the properties of the characteristic function, ivhich is associated ivith the distribution function of the average time of residence [4.28, 4.29]. For this analysis we start ivith the Laplace transformation of the stochastic model ivhen the system (4.31)-(4.32) is considered ... 

The following section contains the particularization of the integral Laplace transformation for the case of the stochastic model given by the assembly of relations (4.146)-(4.147). This particularization illustrates how the Laplace transformation is used to solve partial differential equations. We start by applying the integral Laplace operator to all the terms of relation (4.146) the result is in ... 

The mathematical treatment of stochastic models of bicomponential reactions is rather difficult. The reactions X Yand X Y Z were investigated by Renyi (1953) using Laplace transformation. The method of the generating function does not operate very well in the general case, since it leads to higher-order partial differential equations. In principle chemical... 

---