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There are numerous examples in science and finance in which the process of interest may be subject to some sudden changes in the mean. The process data that are not in a close vicinity of any change point can be analysed by the usual nonparametric smoothing methods. However, the data close to change points and contain the most pertinent information of structural breaks need to be handled with special care. This paper considers a half-kernel approach that addresses the inference of the total number, locations and jump sizes of the changes. Convergence rates and asymptotic distributional results for the proposed procedures are thoroughly investigated. Simulations are conducted to examine the performance of the approach, and a number of real data sets are analysed to provide an illustration.<\/jats:p>","DOI":"10.1111\/rssb.12493","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T08:01:50Z","timestamp":1646812910000},"page":"933-972","source":"Crossref","is-referenced-by-count":6,"title":["On Functional Processes with Multiple Discontinuities"],"prefix":"10.1093","volume":"84","author":[{"given":"Jialiang","family":"Li","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, National University of Singapore , Singapore , Singapore"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yaguang","family":"Li","sequence":"additional","affiliation":[{"name":"School of Management, University of Science and Technology of China , Hefei , 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