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Compound kernel estimates for the transition probability density of a Lévy process in \(\mathbb R^{n}\). (English) Zbl 1322.60057

Theory Probab. Math. Stat. 89, 57-70 (2014); translation from Teor. Jmovirn. Mat. Stat. 89, 51–63 (2013).
Summary: We construct in the small-time setting the upper and lower estimates for the transition probability density of a Lévy process in \(\mathbb{R}^n\). Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse Fourier transform of the characteristic function of the process.

MSC:

60G51 Processes with independent increments; Lévy processes
60J75 Jump processes (MSC2010)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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