ABSTRACT

An estimate on the variation of a random function with the corresponding smooth function is presented in Section 1.1. Section 1.2 deals with the absolute mean deviation of solutions of random polynomial equations with solutions of the corresponding polynomial equations whose coefficients are the mean of the coefficients of the random polynomials. A brief account about the eigenvalues of random matrices and its stability are presented in Sections 1.3 and 1.4, respectively. In Section 1.5, the mathematical results are applied to the problems in (i) economic analysis of capital and investment, and (ii) free damped motion of a spring. In addition, several numerical examples are presented in Section 1.6 illustrating the scope and the usefulness of the mathematical theory.