Foundations of Iso-Differential Calculus

Chapter 1 represents a short introduction to the theory of iso-probability theory. They are defined iso-probability measure, iso-probability space, random iso-variable of the first, second, third, fourth and fifth kind, iso-expected values, iso-martingales, iso-Brownian motion, iso-Wiener processes, Paley-Wiener-Zygmund integral, Itôs iso-integral, and they are deducted some of their properties. Chapter 2 is devoted on the iso-stochastic differential equations of the first, second and third kind, and for them they are proved the general existence and uniqueness theorems. They are given some methods for solving of some classes iso-stochastic differential equations. Chapter 3 deals with the linear iso-stochastic differential equations. The dependence on parameters and initial data is considered in Chapter 4. In Chapter 5 is investigated the stability of the main classes iso-stochastic differential equations. Iso-Stratonovich iso-integral and its properties are considered in Chapter 6.