Latest articles of Modern Stochastics: Theory and Applications
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https://vmsta.org/https://vmsta.org/Latest articles of Modern Stochastics: Theory and Applications
http://vmsta.org/journal/VMSTA/feeds/latest
enThu, 12 Dec 2019 19:11:32 +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<![CDATA[Jackknife covariance matrix estimation for observations from mixture]]>
https://vmsta.org/journal/VMSTA/article/167
https://vmsta.org/journal/VMSTA/article/167A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered. PDFXML]]>A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered. PDFXML]]>Rostyslav Maiboroda,Olena SugakovaThu, 07 Nov 2019 00:00:00 +0200<![CDATA[BSDEs and log-utility maximization for Lévy processes]]>
https://vmsta.org/journal/VMSTA/article/166
https://vmsta.org/journal/VMSTA/article/166In this paper we establish the existence and the uniqueness of the solution of a special class of BSDEs for Lévy processes in the case of a Lipschitz generator of sublinear growth. We then study a related problem of logarithmic utility maximization of the terminal wealth in the filtration generated by an arbitrary Lévy process. PDFXML]]>In this paper we establish the existence and the uniqueness of the solution of a special class of BSDEs for Lévy processes in the case of a Lipschitz generator of sublinear growth. We then study a related problem of logarithmic utility maximization of the terminal wealth in the filtration generated by an arbitrary Lévy process. PDFXML]]>Paolo Di Tella,Hans-Jürgen EngelbertMon, 28 Oct 2019 00:00:00 +0200<![CDATA[On a linear functional for infinitely divisible moving average random fields]]>
https://vmsta.org/journal/VMSTA/article/165
https://vmsta.org/journal/VMSTA/article/165Given a low-frequency sample of the infinitely divisible moving average random field $\{{\textstyle\int _{{\mathbb{R}^{d}}}}f(t-x)\Lambda (dx),\hspace{2.5pt}t\in {\mathbb{R}^{d}}\}$, in [13] we proposed an estimator $\widehat{u{v_{0}}}$ for the function $\mathbb{R}\ni x\mapsto u(x){v_{0}}(x)=(u{v_{0}})(x)$, with $u(x)=x$ and ${v_{0}}$ being the Lévy density of the integrator random measure Λ. In this paper, we study asymptotic properties of the linear functional ${L^{2}}(\mathbb{R})\ni v\mapsto {\left\langle v,\widehat{u{v_{0}}}\right\rangle _{{L^{2}}(\mathbb{R})}}$, 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. PDFXML]]>Given a low-frequency sample of the infinitely divisible moving average random field $\{{\textstyle\int _{{\mathbb{R}^{d}}}}f(t-x)\Lambda (dx),\hspace{2.5pt}t\in {\mathbb{R}^{d}}\}$, in [13] we proposed an estimator $\widehat{u{v_{0}}}$ for the function $\mathbb{R}\ni x\mapsto u(x){v_{0}}(x)=(u{v_{0}})(x)$, with $u(x)=x$ and ${v_{0}}$ being the Lévy density of the integrator random measure Λ. In this paper, we study asymptotic properties of the linear functional ${L^{2}}(\mathbb{R})\ni v\mapsto {\left\langle v,\widehat{u{v_{0}}}\right\rangle _{{L^{2}}(\mathbb{R})}}$, 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. PDFXML]]>Stefan RothTue, 22 Oct 2019 00:00:00 +0300<![CDATA[On estimation of expectation of simultaneous renewal time of time-inhomogeneous Markov chains using dominating sequence]]>
https://vmsta.org/journal/VMSTA/article/164
https://vmsta.org/journal/VMSTA/article/164The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the specific set C by both processes. Under the condition of existence a dominating sequence for both renewal sequences generated by the chains and non-lattice condition for renewal probabilities an upper bound for the expectation of the simultaneous renewal time is obtained. PDFXML]]>The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the specific set C by both processes. Under the condition of existence a dominating sequence for both renewal sequences generated by the chains and non-lattice condition for renewal probabilities an upper bound for the expectation of the simultaneous renewal time is obtained. PDFXML]]>Vitaliy GolomoziyMon, 14 Oct 2019 00:00:00 +0300<![CDATA[Logarithmic Lévy process directed by Poisson subordinator]]>
https://vmsta.org/journal/VMSTA/article/163
https://vmsta.org/journal/VMSTA/article/163Let $\{L(t),t\ge 0\}$ be a Lévy process with representative random variable $L(1)$ defined by the infinitely divisible logarithmic series distribution. We study here the transition probability and Lévy measure of this process. We also define two subordinated processes. The first one, $Y(t)$, is a Negative-Binomial process $X(t)$ directed by Gamma process. The second process, $Z(t)$, is a Logarithmic Lévy process $L(t)$ directed by Poisson process. For them, we prove that the Bernstein functions of the processes $L(t)$ and $Y(t)$ contain the iterated logarithmic function. In addition, the Lévy measure of the subordinated process $Z(t)$ is a shifted Lévy measure of the Negative-Binomial process $X(t)$. We compare the properties of these processes, knowing that the total masses of corresponding Lévy measures are equal. PDFXML]]>Let $\{L(t),t\ge 0\}$ be a Lévy process with representative random variable $L(1)$ defined by the infinitely divisible logarithmic series distribution. We study here the transition probability and Lévy measure of this process. We also define two subordinated processes. The first one, $Y(t)$, is a Negative-Binomial process $X(t)$ directed by Gamma process. The second process, $Z(t)$, is a Logarithmic Lévy process $L(t)$ directed by Poisson process. For them, we prove that the Bernstein functions of the processes $L(t)$ and $Y(t)$ contain the iterated logarithmic function. In addition, the Lévy measure of the subordinated process $Z(t)$ is a shifted Lévy measure of the Negative-Binomial process $X(t)$. We compare the properties of these processes, knowing that the total masses of corresponding Lévy measures are equal. PDFXML]]>Penka Mayster,Assen TchorbadjieffFri, 04 Oct 2019 00:00:00 +0300<![CDATA[Spatial quadratic variations for the solution to a stochastic partial differential equation with elliptic divergence form operator]]>
https://vmsta.org/journal/VMSTA/article/161
https://vmsta.org/journal/VMSTA/article/161We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of diffusion phenomena in medium consisting of different kinds of materials and undergoing stochastic perturbations. We characterize the solution and, using the Stein–Malliavin calculus, we prove that the sequence of its recentered and renormalized spatial quadratic variations satisfies an almost sure central limit theorem. Particular focus is given to the interesting case where the coefficients of the operator are piecewise constant. PDFXML]]>We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of diffusion phenomena in medium consisting of different kinds of materials and undergoing stochastic perturbations. We characterize the solution and, using the Stein–Malliavin calculus, we prove that the sequence of its recentered and renormalized spatial quadratic variations satisfies an almost sure central limit theorem. Particular focus is given to the interesting case where the coefficients of the operator are piecewise constant. PDFXML]]>Mounir Zili,Eya ZougarThu, 03 Oct 2019 00:00:00 +0300