Anticipating exponential processes and stochastic differential equations
Exponential processes in the Ito theory of stochastic integration can be viewed in three aspects: multiplicative renormalization, martingales, and stochastic differential equations. In this paper we initiate the study of anticipating exponential processes from these aspects viewpoints. The analogue of martingale property for anticipating stochastic integrals is the near-martingale property. We use examples to illustrate essential ideas and techniques in dealing with anticipating exponential processes and stochastic differential equations. The situation is very different from the Ito theory.
Publication Source (Journal or Book title)
Communications on Stochastic Analysis
Hwang, C., Kuo, H., & Saitô, K. (2019). Anticipating exponential processes and stochastic differential equations. Communications on Stochastic Analysis, 13 (3-4), 413-424. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/510