Affiliation:
1. Institute for Financial Studies, Shandong University, Jinan 250100, China
2. School of Finance and Business, Shanghai Normal University, Shanghai 200234, China
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.
Funder
Ministry of Education, Humanities and Social Sciences project
National Statistical Science Research Project
Youth Academic Backbone Cultivation Project of Shanghai Normal University
General Research Fund of Shanghai Normal University
Key Subject of Quantitative Economics
Academic Innovation Team of Shanghai Normal University
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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