{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T01:07:37Z","timestamp":1767920857117,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2021,8,1]],"date-time":"2021-08-01T00:00:00Z","timestamp":1627776000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T00:00:00Z","timestamp":1629072000000},"content-version":"vor","delay-in-days":15,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A well-known It\u00f4 formula for finite-dimensional processes, given in terms of stochastic integrals with respect to Wiener processes and Poisson random measures, is revisited and is revised. The revised formula, which corresponds to the classical It\u00f4 formula for semimartingales with jumps, is then used to obtain a generalisation of an important infinite-dimensional It\u00f4 formula for continuous semimartingales from Krylov (Probab Theory Relat Fields 147:583\u2013605, 2010) to a class of <jats:inline-formula><jats:alternatives><jats:tex-math>$$L_p$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mi>p<\/mml:mi>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-valued jump processes. This generalisation is motivated by applications in the theory of stochastic PDEs.\n<\/jats:p>","DOI":"10.1007\/s11134-021-09709-8","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T10:02:57Z","timestamp":1629108177000},"page":"247-273","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On It\u00f4 formulas for jump processes"],"prefix":"10.1007","volume":"98","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2131-1313","authenticated-orcid":false,"given":"Istv\u00e1n","family":"Gy\u00f6ngy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sizhou","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"key":"9709_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809781","volume-title":"L\u00e9vy Processes and Stochastic Calculus","author":"D Applebaum","year":"2009","unstructured":"Applebaum, D.: L\u00e9vy Processes and Stochastic Calculus. 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