M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps |
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Authors: | Yasutaka Shimizu |
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Institution: | (1) Division of Mathematical Science, Graduate School of Engineering Science, Osaka University Toyonaka, Osaka 560-8531, Japan |
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Abstract: | We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations.
We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process
with a Lévy measure fθ(z)dz, and we admit the case ∫ fθ(z)dz = ∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under
this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are
not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and
it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation
results for some simple models.
Final version 25 December 2004 |
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Keywords: | diffusion process with jumps infinitely many jumps M-estimation discrete observation parametric inference asymptotic normality partial efficiency |
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