Modern Stochastics: Theory and Applications
https://www.i-journals.org/vtxpp/VMSTA
<div style="margin-bottom: 10px; display: inline-block;"><span style="margin: 0 5px 11px 0; padding: 5px 11px; color: #356086; background-color: #white; border: 1px solid #6583a5; display: inline-block;"><a style="color: #356086; text-decoration: none; white-space: nowrap;" title="Submit a manuscript" href="https://www.e-publications.org/vtxpp/sbs/VMSTA/author" target="_blank">SUBMIT MANUSCRIPT</a></span> <span style="margin: 0 5px 11px 0; padding: 5px 11px; color: #356086; background-color: #white; border: 1px solid #6583a5; display: inline-block;"><a style="color: #356086; text-decoration: none; white-space: nowrap;" title="Login for Editors" href="https://www.e-publications.org/vtxpp/sbs/VMSTA" target="_blank">LOGIN TO PEER REVIEW SYSTEM</a></span> <span style="margin: 0 5px 11px 0; padding: 5px 11px; color: #356086; background-color: #white; border: 1px solid #6583a5; display: inline-block;"><a style="color: #356086; text-decoration: none; white-space: nowrap;" title="Information for Authors" href="/vtxpp/VMSTA/about/submissions#authorGuidelines" target="_blank">AUTHOR GUIDELINES</a></span></div><table><tbody><tr><td style="width: 60%; padding: 5px 10px 0px 0px; vertical-align: top;"><div style="float: left; margin: 0px 35px 10px 0px;"><a class="action" href="/vtxpp/vmsta"><img style="width: 145px; height: 220px;" src="/vtxpp/public/journals/1/homeHeaderTitleImage_en_US.png" alt="Journal cover" /></a></div><strong>Focus and Scope. </strong><em>Modern Stochastics: Theory and Applications </em>publishes original research papers of highest quality in modern stochastics including<ul><li>probability theory</li><li>mathematical statistics</li><li>theory of stochastic processes and random fields</li><li>stochastic analysis and stochastic differential equations</li><li>probabilistic aspects of fractal analysis</li><li>stochastic geometry</li></ul>and various applied fields such as<br /><ul><li>financial mathematics</li><li>actuarial mathematics and risk theory</li><li>applications in economics, biology, physics, engineering</li><li>optimization and control</li></ul><p>With broad coverage of probability and statistics topics, we welcome original papers to present the deepest and highly innovative results, new tools, ideas and methods with rigorous mathematical background, and also with a great potential for practical applications. Journal will accept only papers of sufficiently high quality both in terms of scientific contents and the presentation of the results (including the graphical aspect of the work). The journal welcomes articles of interdisciplinary nature.</p></td><td style="width: 40%; border-left: 0px solid #adc2d9; padding-left: 20px; vertical-align: top;"><strong>Periodicity.</strong> The journal is published quarterly. <br /><br /><strong>Peer review process.</strong> Articles submitted to VMSTA journal are anonymously reviewed by at least three experts in the field. The details of the peer-review process are described <a href="/vtxpp/VMSTA/about/editorialPolicies#peerReviewProcess">here</a>.<p><strong>Open Access Policy.</strong> This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge.</p><p><strong>Abstracted/Indexed in:</strong> Current Index to Statistics – Extended Database (CIS/ED), Google Scholar, Index Copernicus, MathSciNet, Scilit<strong>, </strong>Zentralblatt MATH Database (zbMATH)<br /><strong>From now – also in: </strong>Emerging Sources Citation Index (ESCI) <span style="color: #444444; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 11.2px;">of Web of Science</span></p><div style="margin: 0px 0 0px 0;"><div style="width: 100px;"><strong>Co-publishing:</strong></div><span style="white-space: nowrap;"> <a title="VTeX. Solutions for Science Publishing" href="http://vtex.lt" target="_blank"> <img style="border: 0px none; width: 115px; height: 80px;" src="/vtxpp/public/journals/1/pageHeaderTitleImage_en_US.png" alt="VTEX. Solutions for Science Publishing" /></a> <a title="Vilnius University" href="http://www.vu.lt/en" target="_blank"> <img style="border: 0px none; width: 69px; height: 80px;" src="/vtxpp/public/site/images/vtxpupl-admin/VU_zenklas.png" alt="Vilnius University" /></a> <a title="Taras Shevchenko National University of Kyiv" href="http://www.univ.kiev.ua/en" target="_blank"> <img style="border: 0px none; width: 80px; height: 80px;" src="/vtxpp/public/site/images/vtxpupl-admin/taras_shevchenko_uni_gerb_small.png" alt="Taras Shevchenko National University of Kyiv" /></a> </span></div><div style="line-height: 0px; margin: 13px 0px 7px 0px; text-align: right;"><a href="/vtxpp/VMSTA/about">More about VMSTA ><span style="margin-left: -3px;">></span></a></div></td></tr></tbody></table><h4 style="margin: 10px 0px -10px 0px; padding: 10px 0px 10px 0px; border-top: 1px solid #adc2d9; border-bottom: 1px solid #adc2d9;"><a style="color: #356086;" href="/vtxpp/VMSTA/issue/view/4">Articles to Appear in Subsequent Issues ><span style="margin-left: -3px;">></span></a></h4>VTeXen-USModern Stochastics: Theory and Applications2351-6046<p>In submitting a manuscript of research article (hereinafter called “Article”) to the “Modern Stochastics: Theory and Applications” journal (hereinafter called “Journal”) published by VTeX (co-Publishers Vilnius University and Taras Shevchenko National University)</p><p>I certify that I am authorized by my co-authors to enter into these arrangements and I guarantee and warrant, on behalf of myself and my co-authors, that:</p><ol><li>I have the full power to enter into this Agreement and to make the grants contained herein. I am/we are the sole author(s) of the article and have full authority to enter into this agreement and in granting rights to VTeX are not in breach of any other obligation.</li><li>The Article is original and does not infringe any copyright or violate any other right of any third parties.</li><li>The Article has not been formally published in any other peer-reviewed journal, is not under consideration by any other journal.</li><li>The Article contains nothing that is unlawful, libellous, or which would, if published, constitute a breach of contract or of confidence or of commitment given to secrecy.</li><li>I agree to the <a href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License 4.0</a> agreement, under the Article in the Journal is licensed and I grant VTeX permission to publish the unpublished and original Article, the abstract forming part thereof, all associated supplemental material, and subsequent, if necessary, errata in the Journal under the Creative Commons Attribution License (CC-BY-4.0).</li><li>Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.</li><li>Anyone is free to share (copy and redistribute the material published in the Article in any medium or format) and adapt (remix, transform, and build upon the material published in the Article) for any purpose, even commercially.</li></ol>The self-normalized Donsker theorem revisited
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA82
We extend the Poincaré–Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Csörgő et al. (2003). Some notes on spheres with respect to $\ell_p$-norms are given.Peter Parczewski2017-09-182017-09-184318919810.15559/17-VMSTA82Asymptotic behavior of functionals of the solutions to inhomogeneous Itô stochastic differential equations with nonregular dependence on parameter
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA83
The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_{0}^{t} g_T(\xi_T(s))\, dW_T(s)$, $t\ge0$ is studied. Here $\xi_T(t)$ is the solution to the time-inhomogeneous Itô stochastic differential equation<br />\[<br />d\xi_T (t)=a_T \bigl(t,\xi_T(t) \bigr)<br />\,dt+dW_T(t),\quad t\ge0,\ \xi_T (0)=x_0,<br />\]<br />$T>0$ is a parameter, $a_T (t,x), x\in\mathbb{R}$ are measurable functions, $ |a_T(t,x)| \leq C_T$ for all $x\in\mathbb{R}$ and $ t\ge0$, $W_T(t)$ are standard Wiener processes, $F_T(x)$, $x\in\mathbb{R}$ are continuous functions, $g_T(x)$, $x\in\mathbb{R}$ are measurable locally bounded functions, and everything is real-valued. The explicit form of the limiting processes for $I_T(t)$ is established under nonregular dependence of $a_T (t,x)$ and $g_T(x)$ on the parameter $T$.Grigorij KulinichSvitlana Kushnirenko2017-09-222017-09-224319921710.15559/17-VMSTA83Quantifying non-monotonicity of functions and the lack of positivity in signed measures
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA84
In various research areas related to decision making, problems and their solutions frequently rely on certain functions being monotonic. In the case of non-monotonic functions, one would then wish to quantify their lack of monotonicity. In this paper we develop a method designed specifically for this task, including quantification of the lack of positivity, negativity, or sign-constancy in signed measures.We note relevant applications in Insurance, Finance, and Economics, and discuss some of them in detail.Youri DavydovRičardas Zitikis2017-09-282017-09-284321923110.15559/17-VMSTA84Weighted entropy: basic inequalities
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA85
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. We analyse analogs of the Fisher information inequality and entropy power inequality for the weighted entropy and discuss connections with weighted Lieb’s splitting inequality. The concepts of rates of the weighted entropy and information are also discussed.Mark KelbertIzabella StuhlYuri Suhov2017-10-022017-10-024323325210.15559/17-VMSTA85Random iterations of homeomorphisms on the circle
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA86
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function systems with probabilities which are non-expansive on average.Katrin GelfertÖrjan Stenflo2017-10-052017-10-054325327110.15559/17-VMSTA86On singularity of distribution of random variables with independent symbols of Oppenheim expansions
https://www.i-journals.org/vtxpp/VMSTA/article/view/VMSTA87
The paper is devoted to the restricted Oppenheim expansion of real numbers ($ROE$), which includes already known Engel, Sylvester and Lüroth expansions as partial cases. We find conditions under which for almost all (with respect to Lebesgue measure) real numbers from the unit interval their $ROE$-expansion contain arbitrary digit $i$ only finitely many times. Main results of the paper state the singularity (w.r.t. the Lebesgue measure) of the distribution of a random variable with i.i.d. increments of symbols of the restricted Oppenheim expansion. General non-i.i.d. case is also studied and sufficient conditions for the singularity of the corresponding probability distributions are found.Liliia SydorukGrygoriy Torbin2017-10-262017-10-264327328310.15559/17-VMSTA87