Information Criteria in Model Selection for Mixing Processes

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Statistical inference for ergodic point processes and application to Limit Order Book (2015, unknown): “A presentation of information criterion-based model selection can be found in the introduction of [38].”
Approximate self-weighted LAD estimation of discretely observed ergodic Ornstein-Uhlenbeck processes (2010, background): “For smooth statistical random fields associated with a stochastic process, large deviation inequalities have been investigated and applied, e.g., to the information criteria in model selection, the validity of higher-order asymptotic statistical theory, and moment convergence for quasi-likelihood an”
Ergodicity and exponential β-mixing bounds for multidimensional diffusions with jumps (2007, methodology): “Indeed, from our results we can directly derive the ergodic theorem, which often plays an essential role for parameter estimation concerning X based on large-time asymptotics; see, e.g., Shimizu [26], Shimizu and Yoshida [27], and Yoshida [34], and see also the simulation study of Masuda [18].”
Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations (2011, background): “Rigorous treatment of this problem under a certain integrability assumption can be seen, e.g., in Uchida and Yoshida (2001) .”