Latest articles of Modern Stochastics: Theory and Applications
http://vmsta.org/journal/VMSTA/feeds/latest
https://vmsta.org/https://vmsta.org/Latest articles of Modern Stochastics: Theory and Applications
http://vmsta.org/journal/VMSTA/feeds/latest
enThu, 27 Jan 2022 23:39:51 +0200<![CDATA[Averaging principle for the one-dimensional parabolic equation driven by stochastic measure]]>
https://vmsta.org/journal/VMSTA/article/233
https://vmsta.org/journal/VMSTA/article/233A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ 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. PDFXML]]>A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ 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. PDFXML]]>Boris ManikinMon, 10 Jan 2022 00:00:00 +0200<![CDATA[Interacting Brownian motions in infinite dimensions related to the origin of the spectrum of random matrices]]>
https://vmsta.org/journal/VMSTA/article/234
https://vmsta.org/journal/VMSTA/article/234The generalised sine random point field arises from the scaling limit at the origin of the eigenvalues of the generalised Gaussian ensembles. We solve an infinite-dimensional stochastic differential equation (ISDE) describing an infinite number of interacting Brownian particles which is reversible with respect to the generalised sine random point field. Moreover, finite particle approximation of the ISDE is shown, that is, a solution to the ISDE is approximated by solutions to finite-dimensional SDEs describing finite-particle systems related to the generalised Gaussian ensembles. PDFXML]]>The generalised sine random point field arises from the scaling limit at the origin of the eigenvalues of the generalised Gaussian ensembles. We solve an infinite-dimensional stochastic differential equation (ISDE) describing an infinite number of interacting Brownian particles which is reversible with respect to the generalised sine random point field. Moreover, finite particle approximation of the ISDE is shown, that is, a solution to the ISDE is approximated by solutions to finite-dimensional SDEs describing finite-particle systems related to the generalised Gaussian ensembles. PDFXML]]>Yosuke KawamotoMon, 10 Jan 2022 00:00:00 +0200<![CDATA[On path-dependent SDEs involving distributional drifts]]>
https://vmsta.org/journal/VMSTA/article/232
https://vmsta.org/journal/VMSTA/article/232The paper presents the study on the existence and uniqueness (strong and in law) of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributions of a continuous function. PDFXML]]>The paper presents the study on the existence and uniqueness (strong and in law) of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributions of a continuous function. PDFXML]]>Alberto Ohashi,Francesco Russo,Alan TeixeiraMon, 03 Jan 2022 00:00:00 +0200<![CDATA[Applications of a change of measures technique for compound mixed renewal processes to the ruin problem]]>
https://vmsta.org/journal/VMSTA/article/231
https://vmsta.org/journal/VMSTA/article/231In the present paper the change of measures technique for compound mixed renewal processes, developed in Tzaninis and Macheras [ArXiv:2007.05289 (2020) 1–25], is applied to the ruin problem in order to obtain an explicit formula for the probability of ruin in a mixed renewal risk model and to find upper and lower bounds for it. PDFXML]]>In the present paper the change of measures technique for compound mixed renewal processes, developed in Tzaninis and Macheras [ArXiv:2007.05289 (2020) 1–25], is applied to the ruin problem in order to obtain an explicit formula for the probability of ruin in a mixed renewal risk model and to find upper and lower bounds for it. PDFXML]]>Spyridon M. TzaninisThu, 23 Dec 2021 00:00:00 +0200<![CDATA[Asymptotic genealogies for a class of generalized Wright–Fisher models]]>
https://vmsta.org/journal/VMSTA/article/229
https://vmsta.org/journal/VMSTA/article/229A class of Cannings models is studied, with population size N having a mixed multinomial offspring distribution with random success probabilities ${W_{1}},\dots ,{W_{N}}$ induced by independent and identically distributed positive random variables ${X_{1}},{X_{2}},\dots $ via ${W_{i}}:={X_{i}}/{S_{N}}$, $i\in \{1,\dots ,N\}$, where ${S_{N}}:={X_{1}}+\cdots +{X_{N}}$. The ancestral lineages are hence based on a sampling with replacement strategy from a random partition of the unit interval into N subintervals of lengths ${W_{1}},\dots ,{W_{N}}$. Convergence results for the genealogy of these Cannings models are provided under assumptions that the tail distribution of ${X_{1}}$ is regularly varying. In the limit several coalescent processes with multiple and simultaneous multiple collisions occur. The results extend those obtained by Huillet [J. Math. Biol. 68 (2014), 727–761] for the case when ${X_{1}}$ is Pareto distributed and complement those obtained by Schweinsberg [Stoch. Process. Appl. 106 (2003), 107–139] for models where sampling is performed without replacement from a supercritical branching process. PDFXML]]>A class of Cannings models is studied, with population size N having a mixed multinomial offspring distribution with random success probabilities ${W_{1}},\dots ,{W_{N}}$ induced by independent and identically distributed positive random variables ${X_{1}},{X_{2}},\dots $ via ${W_{i}}:={X_{i}}/{S_{N}}$, $i\in \{1,\dots ,N\}$, where ${S_{N}}:={X_{1}}+\cdots +{X_{N}}$. The ancestral lineages are hence based on a sampling with replacement strategy from a random partition of the unit interval into N subintervals of lengths ${W_{1}},\dots ,{W_{N}}$. Convergence results for the genealogy of these Cannings models are provided under assumptions that the tail distribution of ${X_{1}}$ is regularly varying. In the limit several coalescent processes with multiple and simultaneous multiple collisions occur. The results extend those obtained by Huillet [J. Math. Biol. 68 (2014), 727–761] for the case when ${X_{1}}$ is Pareto distributed and complement those obtained by Schweinsberg [Stoch. Process. Appl. 106 (2003), 107–139] for models where sampling is performed without replacement from a supercritical branching process. PDFXML]]>Thierry Huillet,Martin MöhleWed, 15 Dec 2021 00:00:00 +0200<![CDATA[Covariance between the forward recurrence time and the number of renewals]]>
https://vmsta.org/journal/VMSTA/article/230
https://vmsta.org/journal/VMSTA/article/230Recurrence times and the number of renewals in $(0,t]$ are fundamental quantities in renewal theory. Firstly, it is proved that the upper orthant order for the pair of the forward and backward recurrence times may result in NWUC (NBUC) interarrivals. It is also demonstrated that, under DFR interarrival times, the backward recurrence time is smaller than the forward recurrence time in the hazard rate order. Lastly, the sign of the covariance between the forward recurrence time and the number of renewals in $(0,t]$ at a fixed time point t and when $t\to \infty $ is studied assuming that the interarrival distribution belongs to certain ageing classes. PDFXML]]>Recurrence times and the number of renewals in $(0,t]$ are fundamental quantities in renewal theory. Firstly, it is proved that the upper orthant order for the pair of the forward and backward recurrence times may result in NWUC (NBUC) interarrivals. It is also demonstrated that, under DFR interarrival times, the backward recurrence time is smaller than the forward recurrence time in the hazard rate order. Lastly, the sign of the covariance between the forward recurrence time and the number of renewals in $(0,t]$ at a fixed time point t and when $t\to \infty $ is studied assuming that the interarrival distribution belongs to certain ageing classes. PDFXML]]>Sotirios LosidisWed, 15 Dec 2021 00:00:00 +0200<![CDATA[Author index]]>
https://vmsta.org/journal/VMSTA/article/226
https://vmsta.org/journal/VMSTA/article/226PDF XML]]>PDF XML]]>Wed, 17 Nov 2021 00:00:00 +0200<![CDATA[Keywords index]]>
https://vmsta.org/journal/VMSTA/article/227
https://vmsta.org/journal/VMSTA/article/227PDF XML]]>PDF XML]]>Wed, 17 Nov 2021 00:00:00 +0200<![CDATA[2010 Mathematics Subject Classification index]]>
https://vmsta.org/journal/VMSTA/article/228
https://vmsta.org/journal/VMSTA/article/228PDF XML]]>PDF XML]]>Wed, 17 Nov 2021 00:00:00 +0200<![CDATA[Principal components analysis for mixtures with varying concentrations]]>
https://vmsta.org/journal/VMSTA/article/222
https://vmsta.org/journal/VMSTA/article/222Principal Component Analysis (PCA) is a classical technique of dimension reduction for multivariate data. When the data are a mixture of subjects from different subpopulations one can be interested in PCA of some (or each) subpopulation separately. In this paper estimators are considered for PC directions and corresponding eigenvectors of subpopulations in the nonparametric model of mixture with varying concentrations. Consistency and asymptotic normality of obtained estimators are proved. These results allow one to construct confidence sets for the PC model parameters. Performance of such confidence intervals for the leading eigenvalues is investigated via simulations. PDFXML]]>Principal Component Analysis (PCA) is a classical technique of dimension reduction for multivariate data. When the data are a mixture of subjects from different subpopulations one can be interested in PCA of some (or each) subpopulation separately. In this paper estimators are considered for PC directions and corresponding eigenvectors of subpopulations in the nonparametric model of mixture with varying concentrations. Consistency and asymptotic normality of obtained estimators are proved. These results allow one to construct confidence sets for the PC model parameters. Performance of such confidence intervals for the leading eigenvalues is investigated via simulations. PDFXML]]>Olena Sugakova,Rostyslav MaiborodaFri, 12 Nov 2021 00:00:00 +0200