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Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence 超过高斯静态序列高水平的点过程的渐近行为
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI: 10.3103/s0027132223060050
V. I. Piterbarg
{"title":"Asymptotic Behavior of Point Processes of Exceeding the High Levels of Gaussian Stationary Sequence","authors":"V. I. Piterbarg","doi":"10.3103/s0027132223060050","DOIUrl":"https://doi.org/10.3103/s0027132223060050","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper studies the asymptotic behavior of point processes of exits of a Gaussian stationary sequence beyond a level tending to infinity more slowly than in the Poisson limit theorem for the number of exits. Convergence in variation of such point processes to a marked Poisson process is proved. The results of Yu.V. Prokhorov on the best approximation of the Bernoulli distribution by a mixture of Gaussian and Poisson distributions are applied. A.N. Kolmogorov proposed this problem in the early 1950s.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300157","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
Sharp Baire Classification of Local Entropy of Parametric Families of Dynamical Systems 动态系统参数族局部熵的锐贝雷分类
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI: 10.3103/s0027132223060086
A. N. Vetokhin
{"title":"Sharp Baire Classification of Local Entropy of Parametric Families of Dynamical Systems","authors":"A. N. Vetokhin","doi":"10.3103/s0027132223060086","DOIUrl":"https://doi.org/10.3103/s0027132223060086","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a parametric family of dynamical systems defined on a locally compact metric space and continuously dependent on a parameter from some metric space. For any such family, the local entropy of the dynamical systems included in it is studied as a function of a parameter from the point of view of the Baire classification of functions.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300439","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 Solution to the Kolmogorov-Feller Equation Arising in a Biological Evolution Model 论生物进化模型中出现的科尔莫戈罗夫-费勒方程的解法
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI: 10.3103/s0027132223060062
O. S. Rozanova
{"title":"On the Solution to the Kolmogorov-Feller Equation Arising in a Biological Evolution Model","authors":"O. S. Rozanova","doi":"10.3103/s0027132223060062","DOIUrl":"https://doi.org/10.3103/s0027132223060062","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers Kolmogorov–Feller equation for the probability density of a Markov process on a half-axis, which arises in important problems of biology. This process consists of random jumps distributed according to the Laplace law and a deterministic return to zero. It is shown that the Green function for such an equation can be found both in the form of a series and in explicit form for some ratios of the parameters. This allows finding explicit solutions to the Kolmogorov–Feller equation for many initial data.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300149","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
Limit Joint Distribution of $$boldsymbol{U}$$ -Statistics, $$boldsymbol{M}$$ -Estimates, and Sample Quantiles $$boldsymbol{U}$$-统计量、$$boldsymbol{M}$$-估计值和样本定量的极限联合分布
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI: 10.3103/s0027132223060074
M. P. Savelov
{"title":"Limit Joint Distribution of $$boldsymbol{U}$$ -Statistics, $$boldsymbol{M}$$ -Estimates, and Sample Quantiles","authors":"M. P. Savelov","doi":"10.3103/s0027132223060074","DOIUrl":"https://doi.org/10.3103/s0027132223060074","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Let <span>(X_{1},X_{2},ldots,X_{n})</span> be independent identically distributed random vectors. Consider a vector <span>(V(X_{1},X_{2},ldots,X_{n}))</span> whose each component is either a <span>(U)</span>-statistic or an <span>(M)</span>-estimator. Sufficient conditions for asymptotic normality of the vector <span>(V(X_{1},X_{2},ldots,X_{n}))</span> are obtained. In the case when <span>(X_{1},X_{2},ldots)</span> are one-dimensional, sufficient conditions for asymptotic normality are obtained for a vector, each component of which is either a <span>(U)</span>-statistic, or an <span>(M)</span>-estimator, or a sample quantile.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300445","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
Discrete-Time Insurance Models 离散时间保险模型
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2024-03-24 DOI: 10.3103/s0027132223060025
E. V. Bulinskaya
{"title":"Discrete-Time Insurance Models","authors":"E. V. Bulinskaya","doi":"10.3103/s0027132223060025","DOIUrl":"https://doi.org/10.3103/s0027132223060025","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Two discrete-time insurance models are considered. The first model studies nonproportional reinsurance and bank loans. For this model, we establish the optimal control and stability to small fluctuation of parameters and perturbation of random variables distributions describing the model. The second model is dual and the ruin probabilities are compared under assumption that the gains distributions satisfy one of four partial orders.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300628","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 Testing the Symmetry of Innovation Distribution in Autoregression Schemes 论检验自回归方案中创新分布的对称性
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2023-12-19 DOI: 10.3103/s0027132223050029
M. V. Boldin, A. R. Shabakaeva
{"title":"On Testing the Symmetry of Innovation Distribution in Autoregression Schemes","authors":"M. V. Boldin, A. R. Shabakaeva","doi":"10.3103/s0027132223050029","DOIUrl":"https://doi.org/10.3103/s0027132223050029","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We consider a stationary linear <span>(AR(p))</span> model with zero mean. The autoregression parameters, as well as the distribution function (d.f.) <span>(G(x))</span> of innovations, are unknown. We test symmetry of innovations with respect to zero in two situations. In the first case the observations are a sample from a stationary solution of <span>(AR(p))</span>. We estimate parameters and find residuals. Based on them we construct a kind of empirical d.f. and the omega-square type test statistic. Its asymptotic d.f. under the hypothesis and the local alternatives are found. In the second situation the observations are subject to gross errors (outliers). For testing the symmetry of innovations we again construct the Pearson’s type statistic and find its asymptotic d.f. under the hypothesis and the local alternatives. We establish the asymptotic robustness of Pearson’s test as well.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742965","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
A Lower Bound on Complexity of a Locator Cellular Automaton Solution for the Closest Neighbor Search Problem 近邻搜索问题的定位蜂窝自动机解法复杂度下限
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2023-12-19 DOI: 10.3103/s0027132223050078
D. I. Vasilev, E. E. Gasanov
{"title":"A Lower Bound on Complexity of a Locator Cellular Automaton Solution for the Closest Neighbor Search Problem","authors":"D. I. Vasilev, E. E. Gasanov","doi":"10.3103/s0027132223050078","DOIUrl":"https://doi.org/10.3103/s0027132223050078","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper considers the application of the locator cellular automaton model to the closest neighbor search problem. The locator cellular automaton model assumes the possibility for each cell to translate a signal through any distance using the ether. It was proven earlier that the ether model allows solving the problem with logarithmic time. In this paper we have derived a logarithmic lower bound for this problem.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138743051","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
Modeling the Degenerate Singularities of Integrable Billiard Systems by Billiard Books 建模可积分台球系统的退化奇点》，台球书籍
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2023-12-19 DOI: 10.3103/s0027132223050030
A. A. Kuznetsova
{"title":"Modeling the Degenerate Singularities of Integrable Billiard Systems by Billiard Books","authors":"A. A. Kuznetsova","doi":"10.3103/s0027132223050030","DOIUrl":"https://doi.org/10.3103/s0027132223050030","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Examples of degenerate (non-Morse-type) multisaddle singularities (atoms) of complexity 1 and multiplicity 3 are realized by integrable billiard books.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742897","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
Spectrum of Schrödinger Operator in Covering of Elliptic Ring 椭圆环覆盖中的薛定谔算子谱
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2023-12-19 DOI: 10.3103/s0027132223050042
M. A. Nikulin
{"title":"Spectrum of Schrödinger Operator in Covering of Elliptic Ring","authors":"M. A. Nikulin","doi":"10.3103/s0027132223050042","DOIUrl":"https://doi.org/10.3103/s0027132223050042","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The stationary Schrödinger equation is studied in a domain bounded by two confocal ellipses and in its coverings. The order of dependence of the Laplace operator eigenvalues on sufficiently small distance between the foci is obtained. Coefficients of the power series expansion of said eigenvalues are calculated up to and including the square of half the focal distance.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742798","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
Constructing the Asymptotics of Solutions to Differential Sturm–Liouville Equations in Classes of Oscillating Coefficients 构建振荡系数类中微分 Sturm-Liouville 方程解的渐近线
IF 0.4
Moscow University Mathematics Bulletin Pub Date : 2023-12-19 DOI: 10.3103/s0027132223050066
N. F. Valeev, E. A. Nazirova, Ya. T. Sultanaev
{"title":"Constructing the Asymptotics of Solutions to Differential Sturm–Liouville Equations in Classes of Oscillating Coefficients","authors":"N. F. Valeev, E. A. Nazirova, Ya. T. Sultanaev","doi":"10.3103/s0027132223050066","DOIUrl":"https://doi.org/10.3103/s0027132223050066","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The article is focused on the development of a method allowing one to construct asymptotics for solutions to ODEs of arbitrary order with oscillating coefficients on the semiaxis. The idea of the method is presented on the example of studying the asymptotics of the Sturm–Liouville equation.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742842","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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