Estimating functions for jump–diffusions

Nina Munkholt Jakobsen*, Michael Sørensen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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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
Issue number9
Pages (from-to)3282-3318
Number of pages37
Publication statusPublished - 2019


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


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