Definition of stochastic differential for distributed time differences and its relationship to tensor products and renormalization groups

Abstract

Stochastic differentials in stochastic differential equations are defined by Ito integrals, however if stochastic differentials and stochastic variations are defined in a mechanical engineering field more better.In this paper, stochastic differentiation as a difference due to distributed time is defined, and clarify its relationship with tensor products and renormalization groups in engineering.The examine the meaning of the Rough path as tensor product , and are obtained the Uncertainty principle in quantum mechanics due to the Rough path based on the renormalization group due to this rough path. Furthermore, the quantum gravity equation is obtained from the rough pass theory.