Using a variation from the construction of the Ornstein-Uhlenbeck process on canonical path-space C ([0 , 1]; R ) in terms of the Brownian sheet, we obtain a large class of processes, adapted to the Brownian filtration, which admit the one dimensional marginals of a martingale.
{"title":"A construction of processes with one dimensional martingale marginals, based upon path-space Ornstein-Uhlenbeck processes and the Brownian sheet","authors":"F. Hirsch, M. Yor","doi":"10.1215/KJM/1256219164","DOIUrl":"https://doi.org/10.1215/KJM/1256219164","url":null,"abstract":"Using a variation from the construction of the Ornstein-Uhlenbeck process on canonical path-space C ([0 , 1]; R ) in terms of the Brownian sheet, we obtain a large class of processes, adapted to the Brownian filtration, which admit the one dimensional marginals of a martingale.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113769","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}
{"title":"On a result of H. Fujimoto","authors":"Xiao-Tian Bai, Q. Han, Ang Chen","doi":"10.1215/KJM/1260975043","DOIUrl":"https://doi.org/10.1215/KJM/1260975043","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1260975043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114132","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}
In the present paper the problems of existence and uniqueness of almost periodic solutions for impulsive Hopfield neural networks are considered. The impulses are in fixed moments of time and by using the technique of estimation of the Cauchy�s matrix new sufficient conditions for the exponential stability of the unique almost periodic solution of such systems are given.
{"title":"Almost periodic models of impulsive Hopfield neural networks","authors":"G. Stamov","doi":"10.1215/KJM/1248983029","DOIUrl":"https://doi.org/10.1215/KJM/1248983029","url":null,"abstract":"In the present paper the problems of existence and uniqueness of almost periodic solutions for impulsive Hopfield neural networks are considered. The impulses are in fixed moments of time and by using the technique of estimation of the Cauchy�s matrix new sufficient conditions for the exponential stability of the unique almost periodic solution of such systems are given.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1248983029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087648","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}
We show a criterion to establish the existence of solutions with prescribed Gevrey wave front sets for pseudodifferential operators of finite order.
给出了有限阶伪微分算子具有给定Gevrey波前集解的存在性判据。
{"title":"Prescribing Gevrey singularities for solutions of pseudodifferential operators","authors":"A. Albanese, P. Popivanov, L. Zanghirati","doi":"10.1215/KJM/1256219157","DOIUrl":"https://doi.org/10.1215/KJM/1256219157","url":null,"abstract":"We show a criterion to establish the existence of solutions with prescribed Gevrey wave front sets for pseudodifferential operators of finite order.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1256219157","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113593","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}
We give some adequate extension, in the framework of a general L´evy process, of our previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The L´evy process framework allows us to streamline our previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. We give some illustrations of our construction when the L´evy process is either a Gamma process, or a Poisson process. We also work in the fractional Brownian and stable frameworks.
{"title":"A construction of processes with one-dimensional martingale marginals, associated with a Lévy process, via its Lévy sheet","authors":"F. Hirsch, M. Yor","doi":"10.1215/KJM/1265899483","DOIUrl":"https://doi.org/10.1215/KJM/1265899483","url":null,"abstract":"We give some adequate extension, in the framework of a general L´evy process, of our previous construction of processes with one-dimensional martingale marginals, done originally in the set-up of Brownian motion. The L´evy process framework allows us to streamline our previous arguments, as well as to reach a larger class of such processes, even in the Brownian case. We give some illustrations of our construction when the L´evy process is either a Gamma process, or a Poisson process. We also work in the fractional Brownian and stable frameworks.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1265899483","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113814","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}
We extend the Mehler-Heine type formula of Jacobi polynomials to a class of multiple orthogonal polynomials of type II. The Mehler-Heine type formulas show standard orthogonal polynomials or multiple orthogonal polynomials near the endpoints of the interval of orthogonality.
{"title":"Certain multiple orthogonal polynomials and a discretization of the Bessel equation","authors":"Tomohiro Takata","doi":"10.1215/KJM/1265899481","DOIUrl":"https://doi.org/10.1215/KJM/1265899481","url":null,"abstract":"We extend the Mehler-Heine type formula of Jacobi polynomials to a class of multiple orthogonal polynomials of type II. The Mehler-Heine type formulas show standard orthogonal polynomials or multiple orthogonal polynomials near the endpoints of the interval of orthogonality.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114251","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}
{"title":"The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels","authors":"Teppei Kobayashi","doi":"10.1215/KJM/1256219158","DOIUrl":"https://doi.org/10.1215/KJM/1256219158","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66113634","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}
{"title":"Construction of a Galois action on modular forms for an arbitrary unitary group","authors":"A. Yamauchi","doi":"10.1215/KJM/1265899477","DOIUrl":"https://doi.org/10.1215/KJM/1265899477","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1265899477","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114181","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}
We extend a locally nilpotent derivation $delta$ on a ring $B$ to $B$-modules $M$ and investigate the properties of such $B$-modules $M$. It turns out that the various geometric properties of the associated $G_a$-action on Spec $B$ can be reflected on the properties of $M$.
{"title":"Locally nilpotent derivations on modules","authors":"Mikiya Tanaka","doi":"10.1215/KJM/1248983033","DOIUrl":"https://doi.org/10.1215/KJM/1248983033","url":null,"abstract":"We extend a locally nilpotent derivation $delta$ on a ring $B$ to $B$-modules $M$ and investigate the properties of such $B$-modules $M$. It turns out that the various geometric properties of the associated $G_a$-action on Spec $B$ can be reflected on the properties of $M$.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087267","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}
{"title":"A shallow water approximation for water waves","authors":"T. Iguchi","doi":"10.1215/KJM/1248983028","DOIUrl":"https://doi.org/10.1215/KJM/1248983028","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1248983028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087634","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}
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