2022-01-29T02:16:05Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000520812021-03-01T16:07:20ZDoubly Uniform Complete Law of Large Numbers for Independent Point ProcessesHattori, Tetsuya155845Law of large numberscomplete convergencecounting processsum of independent random processesWe prove a law of large numbers in terms of uniform complete convergence of independent random variables taking values in functions of $2$ parameters which share similar monotonicity properties as the increments of monotone functions in the initial and the final time parameters. The assumptions for the main result are the H\"older continuity on the expectations as well as moment conditions, while the sample functions may contain jumps.departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2018-06-29application/pdfJournal of Mathematical Sciences The University of Tokyo225171192AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/52081/files/jms250204.pdfeng