Laplace Transform for Stable Random Variables

Laplace transform is a very import conclusion guided by complex function integral, which occupies a very important position in applied mathematics. Especially when solving the initial value problem of n-order linear differential equations with constant coefficients, it is simpler than method of variation of constant and method of undetermined coefficients, and in some cases, it can be used to find the general solution. Based on the definitions and basic theories of the Laplace transform, research on Laplace transform for stable random variables and distribution law of the product of two stable random variables, then prove distribution theorem.