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Generalized Girsanov Transform of Processes and Zakai Equation with Jumps 过程的广义Girsanov变换和带跳跃的Zakai方程
Journal of Stochastic Analysis Pub Date : 2021-09-14 DOI: 10.31390/josa.2.3.17
M. Fujisaki, T. Komatsu
{"title":"Generalized Girsanov Transform of Processes and Zakai Equation with Jumps","authors":"M. Fujisaki, T. Komatsu","doi":"10.31390/josa.2.3.17","DOIUrl":"https://doi.org/10.31390/josa.2.3.17","url":null,"abstract":"It is well known that the Girsanov transform (or, Girsanov's theorem) plays an important role in the stochastic analysis and this transform is closely related with the uniform integrability of local martingales. The ̄rst aim of this article is to give concrete, necessary and su±cient conditions of uniform integrability of positive local martingales with jumps. Then we shall apply Girsanov transform to Zakai equation (Zakai SDE) arisen from the ̄ltering problem of stochastic processes with jumps. Using Girsanov transform for L¶evy processes, Malliavin calculus could be applied to show the existence of smooth density of the ̄ltering measure. The second aim of this article is to show the uniqueness of solutions of Zakai equation. This is worthwhile from the fact that the solution of Zakai equation can be obtained from the ̄ltering measure by using Girsanov transform.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126008776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Uniqueness of Solutions to Martingale Problems for Diffusion Operators with Progressively Measurable Random Coefficients 随机系数逐步可测扩散算子鞅问题解的唯一性
Journal of Stochastic Analysis Pub Date : 2021-09-07 DOI: 10.31390/josa.2.3.16
M. Tsuchiya
{"title":"On the Uniqueness of Solutions to Martingale Problems for Diffusion Operators with Progressively Measurable Random Coefficients","authors":"M. Tsuchiya","doi":"10.31390/josa.2.3.16","DOIUrl":"https://doi.org/10.31390/josa.2.3.16","url":null,"abstract":"The uniqueness of solutions to martingale problems for diffusion operators with progressively measurable coefficients is studied and a uniqueness result is obtained: the uniqueness holds under the conditions of the boundedness and uniform ellipticity for the coefficients of the diffusion operators and under an additional condition for the diffusion coefficients. Construction of appropriate approximation consisting of simple functions to the diffusion coefficients plays a key role; the additional condition is used to ensure the simpleness and then the uniqueness follows from the result in the case of diffusion operators with simple type coefficients, which is due to Stroock and Varadhan.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127330767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An Anti-Symmetric Version of Malliavin Calculus Malliavin微积分的一个反对称版本
Journal of Stochastic Analysis Pub Date : 2021-09-01 DOI: 10.31390/josa.2.3.14
J. Akahori, T. Matsusita, Yasufumi Nitta
{"title":"An Anti-Symmetric Version of Malliavin Calculus","authors":"J. Akahori, T. Matsusita, Yasufumi Nitta","doi":"10.31390/josa.2.3.14","DOIUrl":"https://doi.org/10.31390/josa.2.3.14","url":null,"abstract":". In the present paper we will introduce an anti-symmetric version of Malliavin calculus which consists of operators with anti-commuting relations, which actually form an in(cid:12)nite-dimensional Clifford algebra.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123805920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transfer of Regularity for Markov Semigroups by Using an Interpolation Technique 用插值技术转移马尔可夫半群的正则性
Journal of Stochastic Analysis Pub Date : 2021-08-26 DOI: 10.31390/josa.2.3.13
V. Bally, L. Caramellino
{"title":"Transfer of Regularity for Markov Semigroups by Using an Interpolation Technique","authors":"V. Bally, L. Caramellino","doi":"10.31390/josa.2.3.13","DOIUrl":"https://doi.org/10.31390/josa.2.3.13","url":null,"abstract":"We study the regularity of a Markov semigroup (Pt)t>0, that is, when Pt(x, dy) = pt(x, y)dy for a suitable smooth function pt(x, y). This is done by transferring the regularity from an approximating Markov semigroup sequence (Pn t )t>0, n ∈ N, whose associated densities pt (x, y) are smooth and can blow up as n → ∞. We use an interpolation type result and we show that if there exists a good equilibrium between the blow-up and the speed of convergence, then Pt(x, dy) = pt(x, y)dy and pt has some regularity properties.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115448067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Integration by Parts Formula on Solutions to Stochastic Differential Equations with Jumps on Riemannian Manifolds 黎曼流形上有跳跃的随机微分方程解的分部积分公式
Journal of Stochastic Analysis Pub Date : 2021-08-26 DOI: 10.31390/josa.2.3.12
Hirotaka Kai, Atsushi Takeuchi
{"title":"Integration by Parts Formula on Solutions to Stochastic Differential Equations with Jumps on Riemannian Manifolds","authors":"Hirotaka Kai, Atsushi Takeuchi","doi":"10.31390/josa.2.3.12","DOIUrl":"https://doi.org/10.31390/josa.2.3.12","url":null,"abstract":"Consider solutions to Marcus-type stochastic differential equations with jumps on the bundle of orthonormal frames O(M) over a Riemannian manifold M , and define the M -valued process by its canonical projection, which is parallel to the Eells-Elworthy-Malliavin construction of Brownian motions on M . In the present paper, the integration by parts formula for such jump processes is studied, and the strategy is based upon the calculus on Brownian motions via the Kolmogorov backward equations. The celebrated Bismut formula can be also obtained in our setting.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122882499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Exponential Moments of Additive Processes 关于加性过程的指数矩
Journal of Stochastic Analysis Pub Date : 2021-08-26 DOI: 10.31390/josa.2.3.11
Tsukasa Fujiwara
{"title":"On the Exponential Moments of Additive Processes","authors":"Tsukasa Fujiwara","doi":"10.31390/josa.2.3.11","DOIUrl":"https://doi.org/10.31390/josa.2.3.11","url":null,"abstract":". A theorem on the exponential moments of general R -valued additive processes will be established. A condition that implies the integrability of the exponential of additive processes will be proposed and furthermore the representation of their exponential moments by their characteristics will be shown. In the previous paper [1], the same problem as above has been investigated in the case when the underlying additive processes have the structure of semimartingales. In this paper, another proof for this case will be presented. It will be more inherent and simpler than the previous one. Moreover, the result will be generalized to the case when the underlying additive processes do not necessarily have the structure of semimartingales.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"150 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125435257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Two of Kunita's Papers on Stochastic Flows in Early 1980s 20世纪80年代初Kunita关于随机流的两篇论文
Journal of Stochastic Analysis Pub Date : 2021-08-24 DOI: 10.31390/josa.2.3.09
S. Taniguchi
{"title":"Two of Kunita's Papers on Stochastic Flows in Early 1980s","authors":"S. Taniguchi","doi":"10.31390/josa.2.3.09","DOIUrl":"https://doi.org/10.31390/josa.2.3.09","url":null,"abstract":". Two of Kunita’s papers in early 1980s on diffeomorphic property of stochastic (cid:13)ows are revisited, and corresponding results by the author are presented.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127111967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remembering Kunita-San 记住Kunita-San
Journal of Stochastic Analysis Pub Date : 2021-08-19 DOI: 10.31390/josa.2.3.06
Ken-iti Sato
{"title":"Remembering Kunita-San","authors":"Ken-iti Sato","doi":"10.31390/josa.2.3.06","DOIUrl":"https://doi.org/10.31390/josa.2.3.06","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114674635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Life and Scientific Work of Hiroshi Kunita 国田宏的生平与科学工作
Journal of Stochastic Analysis Pub Date : 2021-08-13 DOI: 10.31390/josa.2.3.05
Y. Ishikawa
{"title":"The Life and Scientific Work of Hiroshi Kunita","authors":"Y. Ishikawa","doi":"10.31390/josa.2.3.05","DOIUrl":"https://doi.org/10.31390/josa.2.3.05","url":null,"abstract":"We describe the life and mathematical work of Hiroshi Kunita and add a few personal recollections which show how admirable person he was.","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125574930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Personal Memories of Hiroshi Kunita 国田宏的个人回忆
Journal of Stochastic Analysis Pub Date : 2021-08-10 DOI: 10.31390/josa.2.3.02
D. Elworthy
{"title":"Personal Memories of Hiroshi Kunita","authors":"D. Elworthy","doi":"10.31390/josa.2.3.02","DOIUrl":"https://doi.org/10.31390/josa.2.3.02","url":null,"abstract":"","PeriodicalId":263604,"journal":{"name":"Journal of Stochastic Analysis","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127518363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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