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Asymptotic inference for stochastic processes

Author

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  • V. Basawa, Ishwar
  • Prakasa Rao, B. L. S.

Abstract

This is a survey of some aspects of large-sample inference for stochastic processes. A unified framework is used to study the asymptotic properties of tests and estimators parameters in discrete-time, continuous-time jump-type, and diffusion processes. Two broad families of processes, viz, ergodic and non-ergodic type are introduced and the qualitative differences in the asymptotic results for the two families are discussed and illustrated with several examples. Some results on estimation and testing via Bayesian, nonparametric, and sequential methods are also surveyed briefly.

Suggested Citation

  • V. Basawa, Ishwar & Prakasa Rao, B. L. S., 1980. "Asymptotic inference for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 10(3), pages 221-254, October.
    • Handle: RePEc:eee:spapps:v:10:y:1980:i:3:p:221-254
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    Cited by:

    1. Justin Sirignano & Konstantinos Spiliopoulos, 2017. "Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem," Papers 1710.04273, arXiv.org, revised Jun 2019.
    2. S. C. Pandhare & T. V. Ramanathan, 2020. "The robust focused information criterion for strong mixing stochastic processes with $$\mathscr {L}^{2}$$ L 2 -differentiable parametric densities," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 637-663, October.

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