期刊
SYMMETRY-BASEL
卷 14, 期 5, 页码 -出版社
MDPI
DOI: 10.3390/sym14050897
关键词
conditional moment; conditional mixed moment; Jacobi process; stochastic correlation process
This paper proposes a simple and novel approach to establish analytical formulas for conditional and mixed moments of the Jacobi process. The approach involves solving a partial differential equation and includes random fluctuations with an asymmetric Wiener process.
This paper proposes a simple and novel approach based on solving a partial differential equation (PDE) to establish the concise analytical formulas for a conditional moment and mixed moment of the Jacobi process with constant parameters, accomplished by including random fluctuations with an asymmetric Wiener process and without any knowledge of the transition probability density function. Our idea involves a system with a recurrence differential equation which leads to the PDE by involving an asymmetric matrix. Then, by using Ito's lemma, all formulas for the Jacobi process with constant parameters as well as time-dependent parameters are extended to the generalized stochastic correlation processes. In addition, their statistical properties are provided in closed forms. Finally, to illustrate applications of the proposed formulas in practice, estimations of parametric methods based on the moments are mentioned, particularly in the method of moments estimators.
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