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
enMon, 06 Apr 2020 19:22:52 +0300<![CDATA[Alternative probabilistic representations of Barenblatt-type solutions]]>
https://vmsta.org/journal/VMSTA/article/177
https://vmsta.org/journal/VMSTA/article/177A general class of probability density functions

is considered, containing as particular case the Barenblatt solutions arising, for instance, in the study of nonlinear heat equations. Alternative probabilistic representations of the Barenblatt-type solutions $u(x,t)$ are proposed. In the one-dimensional case, by means of this approach, $u(x,t)$ can be connected with the wave propagation. PDFXML]]>A general class of probability density functions

is considered, containing as particular case the Barenblatt solutions arising, for instance, in the study of nonlinear heat equations. Alternative probabilistic representations of the Barenblatt-type solutions $u(x,t)$ are proposed. In the one-dimensional case, by means of this approach, $u(x,t)$ can be connected with the wave propagation. PDFXML]]>Alessandro De Gregorio,Roberto GarraMon, 23 Mar 2020 00:00:00 +0200<![CDATA[Stochastic two-species mutualism model with jumps]]>
https://vmsta.org/journal/VMSTA/article/176
https://vmsta.org/journal/VMSTA/article/176The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises. We obtain sufficient conditions for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, strong persistence in the mean and extinction of the solution to the considered system. PDFXML]]>The existence and uniqueness are proved for the global positive solution to the system of stochastic differential equations describing a two-species mutualism model disturbed by the white noise, the centered and non-centered Poisson noises. We obtain sufficient conditions for stochastic ultimate boundedness, stochastic permanence, nonpersistence in the mean, strong persistence in the mean and extinction of the solution to the considered system. PDFXML]]>Olga Borysenko,Oleksandr BorysenkoTue, 03 Mar 2020 00:00:00 +0200<![CDATA[Pathwise asymptotics for Volterra processes conditioned to a noisy version of the Brownian motion]]>
https://vmsta.org/journal/VMSTA/article/175
https://vmsta.org/journal/VMSTA/article/175In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after T, of a Volterra process driven by a Brownian motion in a case where the Brownian motion is not directly observable, but only a noisy version is observed or some linear functionals of the noisy version are observed. Some examples are discussed in both cases. PDFXML]]>In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after T, of a Volterra process driven by a Brownian motion in a case where the Brownian motion is not directly observable, but only a noisy version is observed or some linear functionals of the noisy version are observed. Some examples are discussed in both cases. PDFXML]]>Barbara PacchiarottiThu, 27 Feb 2020 00:00:00 +0200<![CDATA[A characterization of equivalent martingale measures in a renewal risk model with applications to premium calculation principles]]>
https://vmsta.org/journal/VMSTA/article/174
https://vmsta.org/journal/VMSTA/article/174Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound renewal process under Q. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles. PDFXML]]>Generalizing earlier work of Delbaen and Haezendonck for given compound renewal process S under a probability measure P we characterize all probability measures Q on the domain of P such that Q and P are progressively equivalent and S remains a compound renewal process under Q. As a consequence, we prove that any compound renewal process can be converted into a compound Poisson process through a change of measures and we show how this approach is related to premium calculation principles. PDFXML]]>Nikolaos D. Macheras,Spyridon M. TzaninisThu, 20 Feb 2020 00:00:00 +0200<![CDATA[The laws of iterated and triple logarithms for extreme values of regenerative processes]]>
https://vmsta.org/journal/VMSTA/article/173
https://vmsta.org/journal/VMSTA/article/173We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated logarithm for the lim sup and a law of the triple logarithm for the lim inf. This complements a previously known result of Glasserman and Kou [Ann. Appl. Probab. 5(2) (1995), 424–445]. We apply our results to several queuing systems and a birth and death process. PDFXML]]>We analyze almost sure asymptotic behavior of extreme values of a regenerative process. We show that under certain conditions a properly centered and normalized running maximum of a regenerative process satisfies a law of the iterated logarithm for the lim sup and a law of the triple logarithm for the lim inf. This complements a previously known result of Glasserman and Kou [Ann. Appl. Probab. 5(2) (1995), 424–445]. We apply our results to several queuing systems and a birth and death process. PDFXML]]>Alexander Marynych,Ivan MatsakMon, 17 Feb 2020 00:00:00 +0200<![CDATA[Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions]]>
https://vmsta.org/journal/VMSTA/article/172
https://vmsta.org/journal/VMSTA/article/172In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition. PDFXML]]>In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition. PDFXML]]>Yuriy Kozachenko,Enzo Orsingher,Lyudmyla Sakhno,Olga VasylykTue, 17 Dec 2019 00:00:00 +0200<![CDATA[Keywords index]]>
https://vmsta.org/journal/VMSTA/article/168
https://vmsta.org/journal/VMSTA/article/168PDF XML]]>PDF XML]]>Thu, 12 Dec 2019 00:00:00 +0200<![CDATA[Author index]]>
https://vmsta.org/journal/VMSTA/article/169
https://vmsta.org/journal/VMSTA/article/169PDF XML]]>PDF XML]]>Thu, 12 Dec 2019 00:00:00 +0200<![CDATA[2010 Mathematics Subject Classification index]]>
https://vmsta.org/journal/VMSTA/article/170
https://vmsta.org/journal/VMSTA/article/170PDF XML]]>PDF XML]]>Thu, 12 Dec 2019 00:00:00 +0200<![CDATA[Subject index]]>
https://vmsta.org/journal/VMSTA/article/171
https://vmsta.org/journal/VMSTA/article/171PDF XML]]>PDF XML]]>Thu, 12 Dec 2019 00:00:00 +0200