Analysis on the Stochastic Dynamic Field

Abstract

Here, stochastic dynamic field (SDF) is introduced to describe the high stochastic properties of dynamic systems full of various fields. It suggests that there exists measurable space where quantities can be represented and computed. In frame, the space is abstracted as a coordinate system with undetermined dimensions; correspondingly, a quantity (as a high-dimension point) in the coordinate system is a superpositional tensor, i.e., with undetermined relationships between dimensions (indices) or in a random scope in a dimension. As to the certain properties of superpositional tensors in space, gradient, divergence, emission, interactions, as well as the periodicity are modeled, and some classical physical laws such as Euler Equation and Gaussian Law are tried to be transformed with the random factors.