Stochastic Sumudu transform and its applications for solving stochastic differential equations

Abstract This manuscript introduces the development of the stochastic Sumudu transform theory of Itô type for stochastic calculus. We employ the stochastic integration by parts method to achieve this. The purpose of the stochastic Sumudu transform is to solve stochastic differential equations and establish a method for solving them using integral transforms. Furthermore, we derive the Sumudu transforms of commonly used functions in stochastic differential equations. These findings will contribute to the enhancement of literature on stochastic differential equations and have practical applications in fields such as applied mathematics and finance. Additionally, we provide several examples to demonstrate the validity of our work.