Exponential Inequality of Marked Point Processes

Chen Li and Yuping Song ()
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Chen Li: Institute for Financial Studies, Shandong University, Jinan 250100, China
Yuping Song: School of Finance and Business, Shanghai Normal University, Shanghai 200234, China

Mathematics, 2023, vol. 11, issue 4, 1-11

Abstract: This paper presents the uniform concentration inequality for the stochastic integral of marked point processes. We developed a new chaining method to obtain the results. Our main result is presented under an entropy condition for partitioning the index set of the integrands. Our result is an improvement of the work of van de Geer on exponential inequalities for martingales in 1995. As applications of the main result, we also obtained the uniform concentration inequality of functional indexed empirical processes and the Kakutani–Hellinger distance of the maximum likelihood estimator.

Keywords: marked point processes; entropy condition; uniform concentration inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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