{"title":"矩阵值半鞅随机指数的封闭形式公式","authors":"Peter Kern, Christian M�ller","doi":"10.31390/josa.3.2.03","DOIUrl":null,"url":null,"abstract":"We prove a closed form formula for the stochastic exponential of a matrix-valued semimartingale under the assumption that various commutativity conditions are fulfilled. This extends a corresponding result for continuous semimartingales by Yan in [9] to semimartingales with jump parts. We give three examples of a semimartingale in a Lie group setting for which the commutativity conditions are easily verified and explicitly compute their stochastic exponential.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale\",\"authors\":\"Peter Kern, Christian M�ller\",\"doi\":\"10.31390/josa.3.2.03\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a closed form formula for the stochastic exponential of a matrix-valued semimartingale under the assumption that various commutativity conditions are fulfilled. This extends a corresponding result for continuous semimartingales by Yan in [9] to semimartingales with jump parts. We give three examples of a semimartingale in a Lie group setting for which the commutativity conditions are easily verified and explicitly compute their stochastic exponential.\",\"PeriodicalId\":263604,\"journal\":{\"name\":\"Journal of Stochastic Analysis\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Stochastic Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31390/josa.3.2.03\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31390/josa.3.2.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Closed Form Formula for the Stochastic Exponential of a Matrix-Valued Semimartingale
We prove a closed form formula for the stochastic exponential of a matrix-valued semimartingale under the assumption that various commutativity conditions are fulfilled. This extends a corresponding result for continuous semimartingales by Yan in [9] to semimartingales with jump parts. We give three examples of a semimartingale in a Lie group setting for which the commutativity conditions are easily verified and explicitly compute their stochastic exponential.