Non parametric estimation of the jump coefficient of a diffusion with jumps

Émeline Schmisser ()
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Émeline Schmisser: Université de Lille

Statistical Inference for Stochastic Processes, 2025, vol. 28, issue 1, No 6, 32 pages

Abstract: Abstract In this article, we consider a jump diffusion process $$(X_t)_{t \ge 0}$$ ( X t ) t ≥ 0 with drift function b, diffusion coefficient $$\sigma $$ σ and jump coefficient $$\xi $$ ξ . This process is supposed to be ergodic, exponentially $$\beta $$ β -mixing and stationary. It is observed at discrete times $$t=0,\Delta ,\ldots ,n\Delta $$ t = 0 , Δ , … , n Δ . The sampling interval $$\Delta $$ Δ tends to 0 and the time interval $$n\Delta $$ n Δ tends to infinity. We construct a robust, adaptive non-parametric estimator of the function $$\xi ^4$$ ξ 4 thanks to a penalized least-square approach. We provide bounds of the empirical and $$L^2$$ L 2 -risk of our estimator.

Keywords: Jump diffusions; Nonparametric estimation; Model selection; 62G05; 62M05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11203-025-09324-x

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