Maximal inequalities and applications

Research output: Contribution to journalResearch articleContributedpeer-review



A maximal inequality is an inequality which involves the (ab-solute) supremum sups\t |Xs|or the running maximum sups\t Xs of a stochastic process (Xt)t,0. We discuss maximal inequalities for several classes of stochastic processes with values in an Euclidean space: Martin-gales, Levy processes, Levy-type - including Feller processes, (compound) pseudo Poisson processes, stable-like processes and solutions to SDEs driven by a Levy process -, strong Markov processes and Gaussian processes. Us-ing the Burkholder-Davis-Gundy inequalities we also discuss some rela-tions between maximal estimates in probability and the Hardy-Littlewood maximal functions from analysis.


Original languageEnglish
Pages (from-to)382-485
Number of pages4
JournalProbability Surveys
Issue numbernone
Publication statusPublished - 2023

External IDs

WOS 000975036600007
Mendeley 6121dc89-5a06-38b0-b564-5d5a117f0e18



  • And phrases, Burkholder-Davis-Gundy inequality, Concentration function, Doob?s maximal inequality, Feller process, Gaussian process, Good-? inequality, Hardy-Littlewood maximal function, L?vy process, L?vy-type process, Markov process, Martingale inequality, Maximal function, Maximal inequality, Moment estimate, Stochastic differential equation, Tail estimate

Library keywords