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Filterlng of hidden diffusion processes 隐藏扩散过程的滤波
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834267
Hyung Geun Kim
{"title":"Filterlng of hidden diffusion processes","authors":"Hyung Geun Kim","doi":"10.1080/17442500108834267","DOIUrl":"https://doi.org/10.1080/17442500108834267","url":null,"abstract":"Assume xt is a 1-dimensional diffusion process. Suppose xt is exactly observable only when it has negative values, so there is no information when it has nonnegative values. In this paper the filtering equation is derived by using the reverse-time diffusion process. The example of the Wiener process case filtering equation is also presented","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"67 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116026366","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: 3
Limiting points of stochastic flows 随机流的极限点
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834268
M. Liao
{"title":"Limiting points of stochastic flows","authors":"M. Liao","doi":"10.1080/17442500108834268","DOIUrl":"https://doi.org/10.1080/17442500108834268","url":null,"abstract":"It is known that if the flow of a stochastic differential equation on a compact manifold has only negative Lyapunov exponents, then its limiting behavior can be described by a moving random set σof n points. We study the properties of σ and the associated domains of attraction. For example, we will show that it is supported by a compact set on which the induced flow has only one limiting point. On a d-dimensional sphere, if the support of the stochastic flow contains all the isometries, then n=1 or 2, and in the latter case, the two random points and their domains of attractions are antipodal symmetric","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126095246","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
Probabilistic gradient approximation for a viscous scalar conservation law in space dimension d≥2 空间维数d≥2的粘性标量守恒律的概率梯度近似
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834269
B. Jourdain
{"title":"Probabilistic gradient approximation for a viscous scalar conservation law in space dimension d≥2","authors":"B. Jourdain","doi":"10.1080/17442500108834269","DOIUrl":"https://doi.org/10.1080/17442500108834269","url":null,"abstract":"In this paper, we are interested in the solution of a viscous scalar conservation law. We remark that its first order spatial derivatives solve a system of partial differential equations presenting a nonlocal nonlinearity. We associate a nonlinear martingale problem with this system. After proving existence and uniqueness for the martingale problem, we obtain a propagation of chaos result for a system of interacting diffusion processes. We deduce that it is possible to approximate the solution of the viscous scalar conservation law thanks to the interacting diffusions","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131896907","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: 3
Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations 多参数分数布朗运动与拟线性随机偏微分方程
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834263
B. Øksendal, Tusheng Zhang
{"title":"Multiparameter Fractional Brownian Motion And Quasi-Linear Stochastic Partial Differential Equations","authors":"B. Øksendal, Tusheng Zhang","doi":"10.1080/17442500108834263","DOIUrl":"https://doi.org/10.1080/17442500108834263","url":null,"abstract":"We develop a multiparameter white noise theory for fractional Brownian motion with Hurst multiparameter The theory is used to solve the linear and a quasi-linear heat equation driven by multiparameter fractional white noise. It is proved that for some values of H(depending on the dimension) the solution has a jointly continuous version in t and x","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127650889","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: 42
Gaussian ensembles for the nonlinear schrödinger and Kdv equations 非线性schrödinger和Kdv方程的高斯系综
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834265
G. Blower
{"title":"Gaussian ensembles for the nonlinear schrödinger and Kdv equations","authors":"G. Blower","doi":"10.1080/17442500108834265","DOIUrl":"https://doi.org/10.1080/17442500108834265","url":null,"abstract":"Let be the soliton solution to the nonlinear Schrödinger equation on the line. Following the approach of Lebowitz et al. (J. Statist. Phys. 54, 17-56 (1989)) to the periodic case, a family of Gaussian ensembles is introduced. This approximates the Gibbs measure in the sense that it is concentrated on locally bounded functions which are locally uniformly close to the soliton solution. The measure may be normalized when the inverse temperature is sufficiently small. The covariance matrix of the Gaussian process satisfies the Schrödinger equation obtained by linearizing the original equation about the soliton solution. Further, the Gaussian process is stationary with respect to time-shift and spatial translation, in Levitan's sense. Gaussian ensembles for the modified KdV equation are also introduced","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115327967","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 adjoint process of reflected brownian motion in a cone 反射布朗运动在锥体中的伴随过程
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834266
R. D. D. Blassie
{"title":"The adjoint process of reflected brownian motion in a cone","authors":"R. D. D. Blassie","doi":"10.1080/17442500108834266","DOIUrl":"https://doi.org/10.1080/17442500108834266","url":null,"abstract":"We provide two characterizations of the adjoint of reflected Brownian motion in a cone with radially homogeneous reflection. Roughly speaking, the adjoint is another reflected Brownian motion with a drift given by the logarithmic derivative of the invariant measure density and the reflection field is the reflection of the original field across the inward normal","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115439141","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
Dirichlet processes associated to diffusions 与扩散有关的狄利克雷过程
Stochastics and Stochastic Reports Pub Date : 2001-02-01 DOI: 10.1080/17442500108834264
P. Mathieu
{"title":"Dirichlet processes associated to diffusions","authors":"P. Mathieu","doi":"10.1080/17442500108834264","DOIUrl":"https://doi.org/10.1080/17442500108834264","url":null,"abstract":"Let be a reversible diffusion process with values in . We give sufficient conditions on the initial law of W and on a function ƒ for the stochastic process to be a Dirichlet process","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132066605","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: 3
General approach to filtering with fractional brownian noises — application to linear systems 分数阶布朗噪声滤波的一般方法——在线性系统中的应用
Stochastics and Stochastic Reports Pub Date : 2000-12-01 DOI: 10.1080/17442500008834261
M. Kleptsyna, A. Breton, M. Roubaud
{"title":"General approach to filtering with fractional brownian noises — application to linear systems","authors":"M. Kleptsyna, A. Breton, M. Roubaud","doi":"10.1080/17442500008834261","DOIUrl":"https://doi.org/10.1080/17442500008834261","url":null,"abstract":"At first a general approach is proposed to filtering in systems where the observation noise is a fractional Brownian motion. It is shown that the problem can be handled in terms of some appropriate semimartingale and analogs of the classical innovation process and fundamental filtering theorem are obtained. Then the problem of optimal filtering is completely solved for Gaussian linear systems with fractional Brownian noises. Closed form simple equations are derived both for the mean of the optimal filter and the variance of the filtering error. Finally the results are explicited in various specific cases","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"277 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124237535","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: 51
Local Spherical Contact Distribution Function And Local Mean Densities For Inhomogeneous Random Sets 非齐次随机集的局部球面接触分布函数和局部平均密度
Stochastics and Stochastic Reports Pub Date : 2000-12-01 DOI: 10.1080/17442500008834258
V. Capasso, Alessandra Micheletti
{"title":"Local Spherical Contact Distribution Function And Local Mean Densities For Inhomogeneous Random Sets","authors":"V. Capasso, Alessandra Micheletti","doi":"10.1080/17442500008834258","DOIUrl":"https://doi.org/10.1080/17442500008834258","url":null,"abstract":"In this paper we provide definitions for the local mean volume and mean surface densities of an inhomogeneous random closed set A theorem which relates the local spherical contact distribution function with the local surface and volume density is proven. Sufficient conditions on the regularity of the random set involved to satisfy the assumptions of the theorem are provided, based on Coarea Formula. These conditions are satisfied by a wide class of inhomogeneous random sets, relevant for applications, like some kinds of Boolean Models, for which explicit expressions for the local volume and surface densities are also provided","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131466265","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: 18
On the -distance between semimartingales reflecting in different domains> 反射在不同域的半鞅之间的距离[j]
Stochastics and Stochastic Reports Pub Date : 2000-12-01 DOI: 10.1080/17442500008834260
L. Slominski
{"title":"On the -distance between semimartingales reflecting in different domains>","authors":"L. Slominski","doi":"10.1080/17442500008834260","DOIUrl":"https://doi.org/10.1080/17442500008834260","url":null,"abstract":"Let D, D′ be either convex domains in or domains satisfying the conditions (A) and (B) considered by Lions and Sznitman and by Saisho. For given semimartingales Y, Y′ the -distance between solutions of the Skorokhod problem associated with Y, D and Y′, D′ is estimated. Applications to stability problems for stochastic equations with reflecting boundary conditions and to numerical approximation of solutions by the projection scheme and by the discrete penalization scheme are discussed in detail.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114151257","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: 5
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