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Averaging principle for the one-dimensional parabolic equation driven by stochastic measure 随机测量驱动一维抛物方程的平均原理
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2021-01-01 DOI: 10.15559/21-vmsta195
B. Manikin
{"title":"Averaging principle for the one-dimensional parabolic equation driven by stochastic measure","authors":"B. Manikin","doi":"10.15559/21-vmsta195","DOIUrl":"https://doi.org/10.15559/21-vmsta195","url":null,"abstract":"A stochastic parabolic equation on [ 0 ,T ] × R driven by a general stochastic measure is considered. The averaging principle for the equation is established. The convergence rate is compared with other results on related topics.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85265635","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
On path-dependent SDEs involving distributional drifts 关于涉及分布漂移的路径依赖SDEs
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2021-01-01 DOI: 10.15559/21-vmsta197
A. Ohashi, Francesco G. Russo, Alan Teixeira
{"title":"On path-dependent SDEs involving distributional drifts","authors":"A. Ohashi, Francesco G. Russo, Alan Teixeira","doi":"10.15559/21-vmsta197","DOIUrl":"https://doi.org/10.15559/21-vmsta197","url":null,"abstract":"","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"84 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83821608","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
Estimation in a linear errors-in-variables model under a mixture of classical and Berkson errors 经典误差和伯克逊误差混合下线性变量误差模型的估计
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2021-01-01 DOI: 10.15559/21-vmsta186
Mykyta Yakovliev, A. Kukush
{"title":"Estimation in a linear errors-in-variables model under a mixture of classical and Berkson errors","authors":"Mykyta Yakovliev, A. Kukush","doi":"10.15559/21-vmsta186","DOIUrl":"https://doi.org/10.15559/21-vmsta186","url":null,"abstract":"A linear structural regression model is studied, where the covariate is observed with a mixture of the classical and Berkson measurement errors. Both variances of the classical and Berkson errors are assumed known. Without normality assumptions, consistent estimators of model parameters are constructed and conditions for their asymptotic normality are given. The estimators are divided into two asymptotically independent groups.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"89 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83866981","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
Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model 连续时间非线性回归模型残差相关图的渐近正态性
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-12-21 DOI: 10.15559/20-vmsta170
A. Ivanov, K. Moskvychova
{"title":"Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model","authors":"A. Ivanov, K. Moskvychova","doi":"10.15559/20-vmsta170","DOIUrl":"https://doi.org/10.15559/20-vmsta170","url":null,"abstract":"In a continuous time nonlinear regression model the residual correlogram is considered as an estimator of the stationary Gaussian random noise covariance function. For this estimator the functional central limit theorem is proved in the space of continuous functions. The result obtained shows that the limiting sample continuous Gaussian random process coincides with the limiting process in the central limit theorem for standard correlogram of the random noise in the specified regression model.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84137415","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
Long-time behavior of a nonautonomous stochastic predator–prey model with jumps 具有跳跃的非自治随机捕食者-猎物模型的长时间行为
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-12-06 DOI: 10.15559/21-VMSTA173
O. Borysenko, O. Borysenko
{"title":"Long-time behavior of a nonautonomous stochastic predator–prey model with jumps","authors":"O. Borysenko, O. Borysenko","doi":"10.15559/21-VMSTA173","DOIUrl":"https://doi.org/10.15559/21-VMSTA173","url":null,"abstract":"It is proved the existence and uniqueness of the global positive solution to the system of stochastic differential equations describing a non-autonomous stochastic predator-prey model with a modified version of Leslie-Gower and Holling-type II functional response disturbed by white noise, centered and non-centered Poisson noises. We obtain sufficient conditions of stochastic ultimate boundedness, stochastic permanence, non-persistence in the mean, weak persistence in the mean, and extinction of the solution to the considered system.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"106 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80431411","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
Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy 具有随机溢价和常股利策略的风险模型中破产概率的简单逼近
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-08-04 DOI: 10.15559/20-vmsta157
O. Ragulina
{"title":"Simple approximations for the ruin probability in the risk model with stochastic premiums and a constant dividend strategy","authors":"O. Ragulina","doi":"10.15559/20-vmsta157","DOIUrl":"https://doi.org/10.15559/20-vmsta157","url":null,"abstract":"We deal with a generalization of the risk model with stochastic premiums where dividends are paid according to a constant dividend strategy and consider heuristic approximations for the ruin probability. To be more precise, we construct fiveand three-moment analogues to the De Vylder approximation. To this end, we obtain an explicit formula for the ruin probability in the case of exponentially distributed premium and claim sizes. Finally, we analyze the accuracy of the approximations for some typical distributions of premium and claim sizes using statistical estimates obtained by the Monte Carlo methods.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"159 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75968122","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
Applications of a change of measures technique for compound mixed renewal processes to the ruin problem 复合混合更新过程的措施转换技术在废墟问题中的应用
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-07-15 DOI: 10.15559/21-vmsta192
Spyridon M. Tzaninis
{"title":"Applications of a change of measures technique for compound mixed renewal processes to the ruin problem","authors":"Spyridon M. Tzaninis","doi":"10.15559/21-vmsta192","DOIUrl":"https://doi.org/10.15559/21-vmsta192","url":null,"abstract":"In the present paper the change of measures technique for compound mixed renewal processes, developed in Tzaninis & Macheras [24], is applied to the ruin problem in order to compute the ruin probability and to find upper and lower bounds for it.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"22 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87531218","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
Conic intrinsic volumes of Weyl chambers 魏尔腔的圆锥内禀体积
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-05-13 DOI: 10.15559/22-vmsta206
Thomas Godland, Z. Kabluchko
{"title":"Conic intrinsic volumes of Weyl chambers","authors":"Thomas Godland, Z. Kabluchko","doi":"10.15559/22-vmsta206","DOIUrl":"https://doi.org/10.15559/22-vmsta206","url":null,"abstract":"A new, direct proof of the formulas for the conic intrinsic volumes of the Weyl chambers of types ${A_{n-1}}$, ${B_{n}}$ and ${D_{n}}$ is given. These formulas express the conic intrinsic volumes in terms of the Stirling numbers of the first kind and their B- and D-analogues. The proof involves an explicit determination of the internal and external angles of the faces of the Weyl chambers.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88611545","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
Subordinated compound Poisson processes of order k k阶从属复合泊松过程
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-05-01 DOI: 10.15559/20-vmsta165
A. Sengar, N. S. Upadhye
{"title":"Subordinated compound Poisson processes of order k","authors":"A. Sengar, N. S. Upadhye","doi":"10.15559/20-vmsta165","DOIUrl":"https://doi.org/10.15559/20-vmsta165","url":null,"abstract":"In this article, the compound Poisson processes of order $k$ (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinator (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the results in the literature.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"16 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89106926","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
Modeling temporally uncorrelated components of complex-valued stationary processes 复值平稳过程的时间不相关成分建模
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2020-03-09 DOI: 10.15559/21-vmsta190
Niko Lietzén, L. Viitasaari, Pauliina Ilmonen
{"title":"Modeling temporally uncorrelated components of complex-valued stationary processes","authors":"Niko Lietzén, L. Viitasaari, Pauliina Ilmonen","doi":"10.15559/21-vmsta190","DOIUrl":"https://doi.org/10.15559/21-vmsta190","url":null,"abstract":"We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator, that is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag $tau$. Our main contribution is that our asymptotic results can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. We extend this class and consider the unmixing estimator under stronger dependency structures. In particular, we analyze the asymptotic behavior of the unmixing estimator under both, long- and short-range dependent complex-valued processes. Consequently, our theory covers unmixing estimators that converge slower than the usual $sqrt{T}$ and unmixing estimators that produce non-Gaussian asymptotic distributions. The presented methodology is a powerful prepossessing tool and highly applicable in several fields of statistics. Complex-valued processes are frequently encountered in, for example, biomedical applications and signal processing. In addition, our approach can be applied to model real-valued problems that involve temporally uncorrelated pairs. These are encountered in, for example, applications in finance.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"69 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86646558","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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