{"title":"关于可选半鞅的Krylov估计","authors":"M. Abdelghani, A. Melnikov, A. Pak","doi":"10.1515/rose-2021-2059","DOIUrl":null,"url":null,"abstract":"Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"161 - 171"},"PeriodicalIF":0.3000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2021-2059","citationCount":"0","resultStr":"{\"title\":\"On Krylov’s estimates for optional semimartingales\",\"authors\":\"M. Abdelghani, A. Melnikov, A. Pak\",\"doi\":\"10.1515/rose-2021-2059\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.\",\"PeriodicalId\":43421,\"journal\":{\"name\":\"Random Operators and Stochastic Equations\",\"volume\":\"29 1\",\"pages\":\"161 - 171\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/rose-2021-2059\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Random Operators and Stochastic Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/rose-2021-2059\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2021-2059","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
摘要
摘要:对n。V。利用可测函数的L d {L_{d}}范数求解随机积分分布的Krylov方法是众所周知的，并广泛应用于随机微分方程理论和受控扩散过程。我们对可选半鞅推广了这类估计，然后应用这些估计证明了Sobolev空间W d 2 {W^{2}_{d}}中一类一般函数的变量变换公式。我们还展示了如何使用这些估计来研究可选SDE解的l2 {L^{2}}收敛性。
On Krylov’s estimates for optional semimartingales
Abstract The estimates of N. V. Krylov for distributions of stochastic integrals by means of the L d {L_{d}} -norm of a measurable function are well-known and are widely used in the theory of stochastic differential equations and controlled diffusion processes. We generalize estimates of this type for optional semimartingales, then apply these estimates to prove the change of variables formula for a general class of functions from the Sobolev space W d 2 {W^{2}_{d}} . We also show how to use these estimates for the investigation of L 2 {L^{2}} -convergence of solutions of optional SDE’s.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
