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Theory of Probability and Mathematical Statistics最新文献

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Gaussian random fields: with and without covariances 高斯随机场：有和无协变量
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-11-23 DOI: 10.1090/tpms/1163
N. Bingham, T. Symons
{"title":"Gaussian random fields: with and without covariances","authors":"N. Bingham, T. Symons","doi":"10.1090/tpms/1163","DOIUrl":"https://doi.org/10.1090/tpms/1163","url":null,"abstract":"We begin with isotropic Gaussian random fields, and show how the Bochner–Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Matérn processes on Euclidean space, spheres, manifolds and graphs, using Bessel potentials and stochastic partial differential equations (SPDEs). We then turn from this continuous setting to approximating discrete settings, Gaussian Markov random fields (GMRFs), and the computational advantages they bring in handling large data sets, by exploiting the sparseness properties of the relevant precision (concentration) matrices.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45547546","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
Boundedness of the nodal domains of additive Gaussian fields 加性高斯场节点域的有界性
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-11-17 DOI: 10.1090/tpms/1169
S. Muirhead
{"title":"Boundedness of the nodal domains of additive Gaussian fields","authors":"S. Muirhead","doi":"10.1090/tpms/1169","DOIUrl":"https://doi.org/10.1090/tpms/1169","url":null,"abstract":"We study the connectivity of the excursion sets of additive Gaussian fields, i.e. stationary centred Gaussian fields whose covariance function decomposes into a sum of terms that depend separately on the coordinates. Our main result is that, under mild smoothness and correlation decay assumptions, the excursion sets \u0000\u0000 \u0000 \u0000 {\u0000 f\u0000 ≤\u0000 ℓ\u0000 }\u0000 \u0000 {f le ell }\u0000 \u0000\u0000 of additive planar Gaussian fields are bounded almost surely at the critical level \u0000\u0000 \u0000 \u0000 \u0000 ℓ\u0000 c\u0000 \u0000 =\u0000 0\u0000 \u0000 ell _c = 0\u0000 \u0000\u0000. Since we do not assume positive correlations, this provides the first examples of continuous non-positively-correlated stationary planar Gaussian fields for which the boundedness of the nodal domains has been confirmed. By contrast, in dimension \u0000\u0000 \u0000 \u0000 d\u0000 ≥\u0000 3\u0000 \u0000 d ge 3\u0000 \u0000\u0000 the excursion sets have unbounded components at all levels.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47197545","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
Stochastic analysis for vector-valued generalized grey Brownian motion 向量值广义灰布朗运动的随机分析
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-11-17 DOI: 10.1090/tpms/1184
W. Bock, M. Grothaus, Karlo S. Orge
{"title":"Stochastic analysis for vector-valued generalized grey Brownian motion","authors":"W. Bock, M. Grothaus, Karlo S. Orge","doi":"10.1090/tpms/1184","DOIUrl":"https://doi.org/10.1090/tpms/1184","url":null,"abstract":"In this article, we show that the standard vector-valued generalization of a generalized grey Brownian motion (ggBm) has independent components if and only if it is a fractional Brownian motion. In order to extend ggBm with independent components, we introduce a vector-valued generalized grey Brownian motion (vggBm). The characteristic function of the corresponding measure is introduced as the product of the characteristic functions of the one-dimensional case. We show that for this measure, the Appell system and a calculus of generalized functions or distributions are accessible. We characterize these distributions with suitable transformations and give a \u0000\u0000 \u0000 d\u0000 d\u0000 \u0000\u0000-dimensional Donsker’s delta function as an example for such distributions. From there, we show the existence of local times and self-intersection local times of vggBm as distributions under some constraints, and compute their corresponding generalized expectations. At the end, we solve a system of linear SDEs driven by a vggBm noise in \u0000\u0000 \u0000 d\u0000 d\u0000 \u0000\u0000 dimensions.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49499380","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
Infinitesimal invariance of completely Random Measures for 2D Euler Equations 二维欧拉方程完全随机测度的无穷小不变性
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-10-11 DOI: 10.1090/tpms/1178
Francesco Grotto, G. Peccati
{"title":"Infinitesimal invariance of completely Random Measures for 2D Euler Equations","authors":"Francesco Grotto, G. Peccati","doi":"10.1090/tpms/1178","DOIUrl":"https://doi.org/10.1090/tpms/1178","url":null,"abstract":"We consider suitable weak solutions of 2-dimensional Euler equations on bounded domains, and show that the class of completely random measures is infinitesimally invariant for the dynamics. Space regularity of samples of these random fields falls outside of the well-posedness regime of the PDE under consideration, so it is necessary to resort to stochastic integrals with respect to the candidate invariant measure in order to give a definition of the dynamics. Our findings generalize and unify previous results on Gaussian stationary solutions of Euler equations and point vortices dynamics. We also discuss difficulties arising when attempting to produce a solution flow for Euler’s equations preserving independently scattered random measures.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46256299","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: 7
Stochastic heat equation with piecewise constant coefficients and generalized fractional type noise 具有分段常系数和广义分数型噪声的随机热方程
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1150
M. Zili, Eya Zougar
{"title":"Stochastic heat equation with piecewise constant coefficients and generalized fractional type noise","authors":"M. Zili, Eya Zougar","doi":"10.1090/tpms/1150","DOIUrl":"https://doi.org/10.1090/tpms/1150","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41923995","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: 2
A bound in the stable ($alpha $), $1 < alpha le 2$, limit theorem for associated random variables with infinite variance 稳定（$alpha$）中的一个界，$1<alphale2$，具有无穷方差的相关随机变量的极限定理
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1151
M. Sreehari
{"title":"A bound in the stable ($alpha $), $1 < alpha le 2$, limit theorem for associated random variables with infinite variance","authors":"M. Sreehari","doi":"10.1090/tpms/1151","DOIUrl":"https://doi.org/10.1090/tpms/1151","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48403756","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
Estimation of the Hurst and diffusion parameters in fractional stochastic heat equation 分数阶随机热方程中Hurst和扩散参数的估计
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1145
D. A. Avetisian, K. Ralchenko
{"title":"Estimation of the Hurst and diffusion parameters in fractional stochastic heat equation","authors":"D. A. Avetisian, K. Ralchenko","doi":"10.1090/tpms/1145","DOIUrl":"https://doi.org/10.1090/tpms/1145","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45976927","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
On martingale solutions of stochastic partial differential equations with Lévy noise 带lsamvy噪声的随机偏微分方程的鞅解
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1147
V. Mandrekar, U. Naik-Nimbalkar
{"title":"On martingale solutions of stochastic partial differential equations with Lévy noise","authors":"V. Mandrekar, U. Naik-Nimbalkar","doi":"10.1090/tpms/1147","DOIUrl":"https://doi.org/10.1090/tpms/1147","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48040928","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: 24
On existence and uniqueness of the solution for stochastic partial differential equations 随机偏微分方程解的存在唯一性
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-09-24 DOI: 10.1090/tpms/1144
B. Avelin, L. Viitasaari
{"title":"On existence and uniqueness of the solution for stochastic partial differential equations","authors":"B. Avelin, L. Viitasaari","doi":"10.1090/tpms/1144","DOIUrl":"https://doi.org/10.1090/tpms/1144","url":null,"abstract":"","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43406816","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
Extrapolation of stationary random fields via level sets 通过水平集的平稳随机场外推
IF 0.9
Theory of Probability and Mathematical Statistics Pub Date : 2021-08-27 DOI: 10.1090/tpms/1166
Abhinav B. Das, Vitalii Makogin, E. Spodarev
{"title":"Extrapolation of stationary random fields via level sets","authors":"Abhinav B. Das, Vitalii Makogin, E. Spodarev","doi":"10.1090/tpms/1166","DOIUrl":"https://doi.org/10.1090/tpms/1166","url":null,"abstract":"In this paper, we use the concept of excursion sets for the extrapolation of stationary random fields. Doing so, we define excursion sets for the field and its linear predictor, and then minimize the expected volume of the symmetric difference of these sets under the condition that the univariate distributions of the predictor and of the field itself coincide. We illustrate the new approach on Gaussian random fields.","PeriodicalId":42776,"journal":{"name":"Theory of Probability and Mathematical Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41274860","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
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