Consistency of least squares estimation to the parameter for stochastic differential equations under distribution uncertainty

2019/04/29 by Chen Fei, Fei, Chen, Weiyin Fei +1
Decision Sciences · Economics, Econometrics and Finance · #60H10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Risk and Portfolio Optimization #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1904.12701

openalex publication_date 2019/04/29 · openalex created_date 2019/05/03 · openalex updated_date 2026/07/28

Abstract

Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by G-Brownian motion. In order to obtain our main result of consistency of parameter estimation, we provide some lemmas by the theory of stochastic calculus of sublinear expectation. The result shows that under some regularity conditions, the least squares estimator is strong consistent uniformly on the prior set. An illustrative example is discussed.

Citations

• Nonconcave penalized likelihood with a diverging number of parameters
• Optimal stochastic control and optimal consumption and portfolio with G-Brownian motion
• On exponential stability for stochastic differential equations disturbed by G-Brownian motion

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