Help

Home
Search

Modern Stochastics: Theory and Applications

Submit your article Information Become a Peer-reviewer

Journal home
To appear
Current issue
All issues
More
Journal home To appear Current issue All issues

Detailed search

Title

Author

Types

Abstract

Keywords

Published

Pages

Volumes

Issues

DOI

Affiliation

Classifications

Search results 349

Order by:

Select: All None Download:

Multidimensional compound Poisson approximations for symmetric distributions

Vydas Čekanavičius

Simona Jokubauskienė

https://doi.org/10.15559/26-VMSTA301

Pub. online: 26 May 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 4 (2026), pp. 409–431

Abstract

Distribution of the sum of independent identically distributed symmetric lattice vectors is approximated by the accompanying compound Poisson law and the second-order Hipp-type signed compound Poisson measure. Bergström-type asymptotic expansion is constructed. The accuracy of approximation is estimated in the total variation metric and, in many cases, is of the order $O({n^{-1}})$.

Average precision at cutoff k under random rankings: expectation and variance

Tetiana Manzhos

Tetiana Ianevych

Olga Melnyk

https://doi.org/10.15559/26-VMSTA298

Pub. online: 2 Apr 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 357–374

Abstract

Recommender systems and information retrieval platforms rely on ranking algorithms to present the most relevant items to users, thereby improving engagement and satisfaction. Assessing the quality of these rankings requires reliable evaluation metrics. Among them, Mean Average Precision at cutoff k (MAP@k) is widely used, as it accounts for both the relevance of items and their positions in the list for some groups of users.

It seems obvious that intelligent ranking algorithms should outperform recommendations generated at random. But how can we measure how much better they work? In this article, we have established the expected value and variance of the average accuracy at k (AP@k), as they can be used as a foundation for efficiency criteria for MAP@k. Here, we considered two widely used evaluation models: offline and online, together with corresponding randomization models for them, and calculated the expected value and variance of AP@k in both cases. The numerical study for different scenarios was also performed.

Viability for time fractional functional differential equations driven by the fractional Brownian motion

Jingqi Han

Yaqin Sun Litan Yan

https://doi.org/10.15559/26-VMSTA295

Pub. online: 1 Apr 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 303–339

Abstract

Let ${B^{H}}$ be a fractional Brownian motion with Hurst index $\frac{1}{2}\lt H\lt 1$. In this paper, we consider the time fractional functional differential equation of the form

\[ \left\{\begin{array}{l@{\hskip10.0pt}l}{^{C}}{D_{t}^{\gamma }}x(t)=f(t,{x_{t}})+G(t,{x_{t}})\frac{d}{dt}{B^{H}}(t),\hspace{3.33333pt}\hspace{3.33333pt}\hspace{3.33333pt}\hspace{3.33333pt}\hspace{1em}& t\in (0,T],\\ {} {x_{0}}(t)=\eta (t),\hspace{3.33333pt}\hspace{3.33333pt}\hspace{3.33333pt}\hspace{3.33333pt}\hspace{3.33333pt}\hspace{1em}& t\in [-r,0],\end{array}\right.\]

where $\frac{3}{2}-H\lt \gamma \lt 1$, ${^{C}}{D_{t}^{\gamma }}$ denotes the Caputo derivative, and ${x_{t}}\in {\mathcal{C}_{r}}=\mathcal{C}([-r,0],\mathbb{R})$ with ${x_{t}}(u)=x(t+u)$, $u\in [-r,0]$. We prove the global existence and uniqueness of the solution of the equation and study its viability. As an application, we also discuss the existence of positive solutions.

Some continuity estimates for ruin probability and other ruin-related quantities

Lazaros Kanellopoulos

https://doi.org/10.15559/26-VMSTA300

Pub. online: 26 Mar 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 387–407

Abstract

In this paper we investigate continuity properties for ruin probability in the classical risk model. Properties of contractive integral operators are used to derive continuity estimates for the deficit at ruin. These results are also applied to obtain desired continuity inequalities in the setting of continuous time surplus process perturbed by diffusion. In this framework, the ruin probability can be expressed as the convolution of a compound geometric distribution K with a diffusion term. A continuity inequality for K is derived and an iterative approximation for this ruin-related quantity is proposed. The results are illustrated by numerical examples.

The generalization of several classical estimators for a positive extreme value index

Marijus Vaičiulis

https://doi.org/10.15559/26-VMSTA296

Pub. online: 19 Mar 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 341–355

Abstract

In this paper, we introduce a family of semi-parametric estimators for the positive extreme value index γ, parameterized in two tuning parameters. The asymptotic normality of the introduced estimators is proved. It is shown that the partial case of newly introduced estimators (a subfamily with one tuning parameter) has quite good asymptotic properties and dominates several previously introduced estimators. Small Monte-Carlo simulations are included. Also, the performance of this parameterized subfamily of estimators is illustrated for pair exchange ratio data sets.

Convergence of random walks in

ℓ_{p}

-spaces of growing dimension

Bochen Jin

https://doi.org/10.15559/26-VMSTA299

Pub. online: 12 Mar 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 375–385

Abstract

We prove a limit theorem for paths of random walks with n steps in ${\mathbb{R}^{d}}$ as n and d both go to infinity. For this, the paths are viewed as finite metric spaces equipped with the ${\ell _{p}}$-metric for $p\in [1,\infty )$. Under the assumptions that all components of each step are uncorrelated, centered, have finite $2p$-th moments, and are identically distributed, we show that such random metric space converges in probability to a deterministic limit space with respect to the Gromov-Hausdorff distance. This result generalises earlier work by Kabluchko and Marynych [Ann. Inst. H. Poincaré Probab. Statist. 60(4): 2945–2974, 2024] for $p=2$.

A Chinese restaurant process for multiset permutations

Dudley Stark

https://doi.org/10.15559/26-VMSTA294

Pub. online: 3 Mar 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 289–301

Abstract

Multisets are like sets, except that they can contain multiple copies of their elements. If there are ${n_{i}}$ copies of i, $1\le i\le t$, in multiset ${M_{t}}$, then there are $\left(\genfrac{}{}{0.0pt}{}{{n_{1}}+\cdots +{n_{t}}}{{n_{1}},\dots ,{n_{t}}}\right)$ possible permutations of ${M_{t}}$. Knuth showed how to factor any multiset permutation into cycles. For fixed ${n_{i}}$, $i\ge 1$, we show how to adapt the Chinese restaurant process, which generates random permutations on n elements with weighting ${\theta ^{\# \hspace{0.1667em}\mathrm{cycles}}}$, $\theta \gt 0$, sequentially for $n=1,2,\dots $, to the multiset case, where we fix the ${n_{i}}$ and build permutations on ${M_{t}}$ sequentially for $t=1,2,\dots $. The number of cycles of a multiset permutation chosen uniformly at random, i.e. $\theta =1$, has distribution given by the sum of independent negative hypergeometric distributed random variables. For all $\theta \gt 0$, and under the assumption that ${n_{i}}=O(1)$, we show a central limit theorem as $t\to \infty $ for the number of cycles.

Editorial

Wolfgang Bock

Kȩstutis Kubilius

Yuliya Mishura

Kostiantyn Ralchenko

https://doi.org/10.15559/26-VMSTA297

Pub. online: 3 Mar 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 2 (2026): Fractional Calculus, Fractional Processes, and Long-Range Dependence, pp. 147–148

Submartingale condition for weak convergence for semi-Markov processes

Vitaliy Golomoziy

https://doi.org/10.15559/26-VMSTA293

Pub. online: 24 Feb 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 3 (2026), pp. 275–287

Abstract

In this paper, we consider a modified version of a well-known submartingale condition for the weak convergence of probability measures, adapted to the semi-Markov case. In this setting, it is convenient to work with an embedded Markov chain and the filtration generated by jump times. We demonstrate that a straightforward restatement of the classical result is not valid, and that an additional condition is required.

The Ornstein–Uhlenbeck process driven by the Hermite–Ornstein–Uhlenbeck process

Charles-Philippe Diez Ciprian A. Tudor

https://doi.org/10.15559/26-VMSTA292

Pub. online: 10 Feb 2026 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 13, Issue 2 (2026): Fractional Calculus, Fractional Processes, and Long-Range Dependence, pp. 255–273

Abstract

In this paper, a non-Gaussian Ornstein–Uhlenbeck process driven by a Hermite–Ornstein–Uhlenbeck process is introduced, which belongs to the qth Wiener chaos. A systematic procedure to identify the drift parameter θ and the Hurst parameter H is given based on the study of the limit behavior of its quadratic variations. Estimators for these two parameters and their asymptotic properties are studied.

1 2 3 4

Items per page

Export citation

Copy and paste formatted citation

Formatted citation

Placeholder

Citation style

Download citation in file

Export format

Authors

Placeholder

RSS

MSTA

Journal

Online ISSN: 2351-6054
Print ISSN: 2351-6046

About

About journal
Indexed in
Editors-in-Chief

For contributors

Submit
OA Policy
Become a Peer-reviewer

Contact us

ejournals-vmsta@vtex.lt
Mokslininkų 2A
LT-08412 Vilnius
Lithuania