A simple way of introducing stochastic differential equations

19th International Youth School on Coherent Optics and Optical Spectroscopy

Basharov, A.M.^1,2

Moscow Institute of Physics and Technology, Dolgoprudny

141700, Russia^1

National Research Centre Kurchatov Institute, Moscow

123182, Russia^2

关键词: Counting process;    Stochastic differential equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/714/1/012004/pdf
DOI  :  10.1088/1742-6596/714/1/012004

来源: IOP

【 摘 要 】

The notion of the Ito increment and the stochastic differential equation of the non-Wiener type were introduced using the simple "natural" property of counting process. The properties of the stochastic differential and integral were demonstrated and clarified in a simple and original way.