{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:43:51Z","timestamp":1787341431734,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"National Key Research and Development Program of China","award":["2023YFA1009100"],"award-info":[{"award-number":["2023YFA1009100"]}]},{"name":"National Key Research and Development Program of China","award":["12071430"],"award-info":[{"award-number":["12071430"]}]},{"name":"National Key Research and Development Program of China","award":["12525112"],"award-info":[{"award-number":["12525112"]}]},{"DOI":"10.13039\/501100004835","name":"Zhejiang University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004835","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"crossref","award":["12371421"],"award-info":[{"award-number":["12371421"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2025,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This paper concerns the inverse source problem for the stochastic eddy current equations driven by white noise. The random source is vector-valued,\u00a0and the white noise in each component is different and dependent on each other. Quantitative stability estimates are derived for the inverse problem of determining the variance of the random source at a fixed frequency. Moreover, we show that the stability estimates improve as the frequency increases, which exhibit the phenomenon of increasing stability. The analysis employs It\u00f4\u2019s isometry and construction of complex exponential solutions. The eddy current equations considered in this paper are also closely related to the frequency-domain diffusion equation which arises in the field of optical tomography.<\/jats:p>","DOI":"10.1137\/24m170003x","type":"journal-article","created":{"date-parts":[[2025,11,13]],"date-time":"2025-11-13T08:17:35Z","timestamp":1763021855000},"page":"1972-1989","source":"Crossref","is-referenced-by-count":0,"title":["Stability for a Stochastic Inverse Source Problem in Eddy Current Equations"],"prefix":"10.1137","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9699-780X","authenticated-orcid":true,"given":"Tianjiao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0626-7609","authenticated-orcid":true,"given":"Xiang","family":"Xu","sequence":"additional","affiliation":[{"name":"Center for Interdisciplinary Applied Mathematics, and School of Mathematical Sciences, Zhejiang University, Hangzhou, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Zhao","sequence":"additional","affiliation":[{"name":"Corresponding author. School of Mathematics and Statistics, and Key Lab NAA\u2013MOE, Central China Normal University, Wuhan, 430079 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,11,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-09-02254-6"},{"key":"ref2","volume-title":"Sobolev Spaces","author":"Adams R.","year":"2003","edition":"2"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139998348979"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141098343604"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1364\/OL.23.000882"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/050647177"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/16M1067470"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/16M1088922"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2019.06.006"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/19M1282866"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/23M1628334"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141001383564"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-02-01468-0"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/23M1586331"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/20M1331342"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/19M1309456"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1137\/040619193"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1364\/AO.46.006669"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/28\/1\/015006"},{"key":"ref20","volume-title":"Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals","author":"Stein E.","year":"1993"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1137\/24M1655974"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-006-0008-3"}],"container-title":["SIAM\/ASA Journal on Uncertainty Quantification"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M170003X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:19:23Z","timestamp":1787339963000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M170003X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,13]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12,31]]}},"alternative-id":["10.1137\/24M170003X"],"URL":"https:\/\/doi.org\/10.1137\/24m170003x","relation":{},"ISSN":["2166-2525"],"issn-type":[{"value":"2166-2525","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,13]]}}}