Estimating functions for jump–diffusions

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Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate-optimality and efficiency are of particular concern. Under mild assumptions, it is shown that estimators of drift, diffusion, and jump parameters are consistent and asymptotically normal, as well as rate-optimal for the drift and jump parameters. Additional conditions are derived, which ensure rate-optimality for the diffusion parameter as well as efficiency for all parameters. The findings indicate a potentially fruitful direction for the further development of estimation for jump–diffusions.

Original languageEnglish
JournalStochastic Processes and Their Applications
Pages (from-to)3282–3318
Publication statusPublished - 2019

    Research areas

  • Approximate martingale estimating function, Diffusion with jumps, Discrete-time sampling, Efficiency, Optimal rate, Stochastic differential equation

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