Construction of special soliton solutions to the stochastic Riccati equation

Abstract A scheme for the analytical stochastization of ordinary differential equations (ODEs) is presented in this article. Using Itô calculus, an ODE transformed into a stochastic equation (SDE) such way that solutions obtained can be constructed. Furthermore, constructed trajectories remain bounded same interval as deterministic solutions. The proposed approach stark contrast to methods based on randomization solution and not focused analysis martingales. This article extends theory calculus by directly implementing it schemes generalized operator differentiation. efficacy techniques demonstrated deriving soliton Riccati equation. semi-analytical relevant investigation global dynamics different biological biomedical processes where variation predetermined rationale model.