Stochastic motion under G-framework: II. Kinematics |
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Authors: | Hong Zhang |
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Institution: | Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh, Wisconsin, USA |
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Abstract: | Continuing the study of stochastic motion that we started 11 Zhang, H., and Kannan, D. 2014. Stochastic motion under G-framework: I. Nelson stochastic derivatives. Stoch Anal Appl 32:1067–1096.Taylor & Francis Online], Web of Science ®] , Google Scholar]], we present in this article the kinematics of such a motion. We begin by defining the quadratic derivative of an S2-process, and show that this derivative of the Brownian motion captures the variance uncertainty. We show, under certain vanishing derivatives and independence conditions, the martingale properties of an S1-process. Starting with an S1-process, we derive the equation of motion, an Itô equation corresponding to a G-diffusion process. |
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Keywords: | Quadratic derivatives S0- S1- S2-processes martingale difference kinematics G-Itô equation |
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