Non parametric estimation of the diffusion coefficients of a diffusion with jumps

Émeline Schmisser

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 5364-5405

Abstract: In this article, we consider a jump diffusion process Xtt≥0, with drift function b, diffusion coefficient σ and jump coefficient ξ2. This process is observed at discrete times t=0,Δ,…,nΔ. The sampling interval Δ tends to 0 and the time interval nΔ tends to infinity. We assume that Xtt≥0 is ergodic, strictly stationary and exponentially β-mixing. We use a penalized least-square approach to compute adaptive estimators of the functions σ2+ξ2 and σ2. We provide bounds for the risks of the two estimators.

Keywords: Jump diffusions; Model selection; Nonparametric estimation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2019.03.003

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