GRONWALL-TYPE MOMENT INEQUALITIES FOR A STOCHASTIC PROCESS

The main purpose of this paper is to demonstrate the moment inequality theorems of the stochastic process. More specifically, we want to establish some stochastic moment inequalities in the stochastic process by applying the Ito formula and the Gronwall-type inequalities as well as introduce a new proofs of some parts of the Burkholder-Davis-Gundy inequality and induce inverse inequality.

Automated summary

The main purpose of this paper is to demonstrate the moment inequality theorems in stochastic processes. Specifically, the paper aims to establish stochastic moment inequalities using the Ito formula and the Gronwall-type inequalities. It also introduces new proofs for some parts of the Burkholder-Davis-Gundy inequality and derivation of the inverse inequality.