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Asymptotics for the sum of three state Markov dependent random variables 三态马尔可夫相关随机变量和的渐近性
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-11-19 DOI: 10.15559/18-VMSTA123
Gabija Liaudanskait.e, V. vCekanavivcius
{"title":"Asymptotics for the sum of three state Markov dependent random variables","authors":"Gabija Liaudanskait.e, V. vCekanavivcius","doi":"10.15559/18-VMSTA123","DOIUrl":"https://doi.org/10.15559/18-VMSTA123","url":null,"abstract":"The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the aggregate claims distribution after $nin mathbb {N}$ periods. The accuracy of order $O(n^{-1})$ and $O(n^{-1/2})$ is obtained for the local and uniform norms, respectively. In a particular case, the accuracy of estimates in total variation and non-uniform estimates are shown to be at least of order $O(n^{-1})$. The characteristic function method is used. The results can be applied to estimate the probable loss of an insurer to optimize an insurance premium.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"20 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80625697","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 a linear functional for infinitely divisible moving average random fields 无限可分移动平均随机场的线性泛函
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-10-21 DOI: 10.15559/19-VMSTA143
Stefan Roth
{"title":"On a linear functional for infinitely divisible moving average random fields","authors":"Stefan Roth","doi":"10.15559/19-VMSTA143","DOIUrl":"https://doi.org/10.15559/19-VMSTA143","url":null,"abstract":"Given a low-frequency sample of the infinitely divisible moving average random field ${int_{mathbb{R}^d}f(t-x)Lambda (dx), tin mathbb{R}^d}$, in [13] we proposed an estimator $hat{uv_0}$ for the function $mathbb{R}ni xmapsto u(x)v_0(x)=(uv_0)(x)$, with $u(x)=x$ and $v_0$ being the L'{e}vy density of the integrator random measure $Lambda$. In this paper, we study asymptotic properties of the linear functional $L^2(mathbb{R})ni vmapsto left langle v,hat{uv_0}right rangle_{L^2(mathbb{R})}$, if the (known) kernel function $f$ has a compact support. We provide conditions that ensure consistency (in mean) and prove a central limit theorem for it.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"90 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79738716","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
Ruin probability for the bi-seasonal discrete time risk model with dependent claims 具有从属索赔的双季节离散时间风险模型的破产概率
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-10-01 DOI: 10.15559/18-VMSTA118
Olga Navickien.e, Jonas Sprindys, Jonas vSiaulys
{"title":"Ruin probability for the bi-seasonal discrete time risk model with dependent claims","authors":"Olga Navickien.e, Jonas Sprindys, Jonas vSiaulys","doi":"10.15559/18-VMSTA118","DOIUrl":"https://doi.org/10.15559/18-VMSTA118","url":null,"abstract":"The discrete time risk model with two seasons and dependent claims is considered. An algorithm is created for computing the values of the ultimate ruin probability. Theoretical results are illustrated with numerical examples.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"281 3 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86575889","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: 4
Arithmetic of (independent) sigma-fields on probability spaces 概率空间上(独立)sigma域的算法
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-09-14 DOI: 10.15559/19-VMSTA135
M. Vidmar
{"title":"Arithmetic of (independent) sigma-fields on probability spaces","authors":"M. Vidmar","doi":"10.15559/19-VMSTA135","DOIUrl":"https://doi.org/10.15559/19-VMSTA135","url":null,"abstract":"This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated $sigma$-field'', and of ``complementation'' for (independent) complete $sigma$-fields on probability spaces.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"6 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79091251","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
Moderate deviations for a stochastic Burgers equation 随机Burgers方程的中等偏差
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-07-24 DOI: 10.15559/19-VMSTA134
R. Belfadli, Lahcen Boulanba, M. Mellouk
{"title":"Moderate deviations for a stochastic Burgers equation","authors":"R. Belfadli, Lahcen Boulanba, M. Mellouk","doi":"10.15559/19-VMSTA134","DOIUrl":"https://doi.org/10.15559/19-VMSTA134","url":null,"abstract":"A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"33 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88530586","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: 9
Note on AR(1)-characterisation of stationary processes and model fitting 关于AR(1)的说明——平稳过程的表征和模型拟合
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-05-28 DOI: 10.15559/19-VMSTA132
M. Voutilainen, L. Viitasaari, Pauliina Ilmonen
{"title":"Note on AR(1)-characterisation of stationary processes and model fitting","authors":"M. Voutilainen, L. Viitasaari, Pauliina Ilmonen","doi":"10.15559/19-VMSTA132","DOIUrl":"https://doi.org/10.15559/19-VMSTA132","url":null,"abstract":"It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article we provide a detailed analysis of these special cases. In particular, we prove that these cases correspond to degenerate processes.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"123 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74684517","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: 9
On distributions of exponential functionals of the processes with independent increments 具有独立增量过程的指数泛函分布
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-04-19 DOI: 10.15559/20-vmsta159
L. Vostrikova
{"title":"On distributions of exponential functionals of the processes with independent increments","authors":"L. Vostrikova","doi":"10.15559/20-vmsta159","DOIUrl":"https://doi.org/10.15559/20-vmsta159","url":null,"abstract":"The aim of this paper is to study the laws of the exponential functionals of the processes $X$ with independent increments, namely $$I_t= int _0^texp(-X_s)ds, ,, tgeq 0,$$ and also $$I_{infty}= int _0^{infty}exp(-X_s)ds.$$ Under suitable conditions we derive the integro-differential equations for the density of $I_t$ and $I_{infty}$. We give sufficient conditions for the existence of smooth density of the laws of these functionals. In the particular case of Levy processes these equations can be simplified and, in a number of cases, solved explicitly.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83635189","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: 4
Studies on generalized Yule models 广义Yule模型的研究
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-03-20 DOI: 10.15559/18-VMSTA125
F. Polito
{"title":"Studies on generalized Yule models","authors":"F. Polito","doi":"10.15559/18-VMSTA125","DOIUrl":"https://doi.org/10.15559/18-VMSTA125","url":null,"abstract":"We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the $OS$ property, while for the growth of species we use nonlinear time-fractional pure birth processes. Further, in two specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time $t$. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"190 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83058674","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
Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates 一类交替速率整数上连续时间马尔可夫链的随机时变及渐近结果
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-02-18 DOI: 10.15559/20-vmsta169
L. Beghin, C. Macci, B. Martinucci
{"title":"Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates","authors":"L. Beghin, C. Macci, B. Martinucci","doi":"10.15559/20-vmsta169","DOIUrl":"https://doi.org/10.15559/20-vmsta169","url":null,"abstract":"We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subodinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in Di Crescenzo A., Macci C., Martinucci B. (2014).","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"203 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88029874","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 tail behaviour of stationary second-order Galton–Watson processes with immigration 带迁移的平稳二阶Galton-Watson过程的尾部行为
IF 0.4
Modern Stochastics-Theory and Applications Pub Date : 2018-01-24 DOI: 10.15559/20-VMSTA161
M. Barczy, Z. Bősze, G. Pap
{"title":"On tail behaviour of stationary second-order Galton–Watson processes with immigration","authors":"M. Barczy, Z. Bősze, G. Pap","doi":"10.15559/20-VMSTA161","DOIUrl":"https://doi.org/10.15559/20-VMSTA161","url":null,"abstract":"A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a second-order Galton-Watson process with immigration under which the corresponding 2-type Galton-Watson process with immigration has a unique stationary distribution such that its common marginals are regularly varying. In the course of the proof sufficient conditions are given under which the distribution of a second-order Galton-Watson process (without immigration) at any fixed time is regularly varying provided that the initial sizes of the population are independent and regularly varying.","PeriodicalId":42685,"journal":{"name":"Modern Stochastics-Theory and Applications","volume":"414 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84893557","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: 4
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