Abstract
In this work, we consider a prototype stochastic dynamic model for dynamic processes in biological, chemical, economic, financial, medical, military, physical and technological sciences. The dynamic model is described by Lévy-type nonlinear stochastic differential equation. The model validation is established by the usage of Lyapunov-like function. The basic innovative idea is to transform a nonlinear Lévy-type nonlinear stochastic differential into a simpler stochastic differential equation that is easily tested for the existence and uniqueness theorem. Using the nature of Lyapunov-like function, the existence and uniqueness of solution of the original Lévy-type nonlinear stochastic differential equation is established. The main idea of the proof is based on the property of the one-to-one and onto transformation. As the byproduct of the analysis, it is shown that the closed-form implicit solution of transformed stochastic differential equation is a positive martingale. Furthermore, using the change of measure, a Girsanov-type theorem for Lévy-type nonlinear stochastic dynamic model is established.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
