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NEW ARTICLE

System Administrator

https://doi.org/10.1000/222

Pub. online: 30 Aug 2021 Type: Article

Journal: Modern Stochastics: Theory and Applications Volumes 1-2, Issues 1-2 (2021): Test, pp. 1–2222

NEW ARTICLE

System Administrator

https://doi.org/10.2000/2224

Pub. online: 30 Aug 2021 Type: Article

Journal: Modern Stochastics: Theory and Applications Volumes 1-2, Issues 1-2 (2021): Test, pp. 1–2222

Discussion 31/08/21

System Administrator

https://doi.org/10.1000/2229888

Pub. online: 30 Aug 2021 Type: Discussion

Journal: Modern Stochastics: Theory and Applications Volumes 1-5, Issues 1-3 (2021): Test2, pp. 1–200

Final version of Dataset Title

System Administrator Наталья Test

https://doi.org/3123123

Pub. online: 18 Aug 2021 Type: Article

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–100

Optimal transport between determinantal point processes and application to fast simulation

Laurent Decreusefond

Guillaume Moroz

https://doi.org/10.15559/21-VMSTA180

Pub. online: 2 Jun 2021 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–29

Abstract

Two optimal transport problems between determinantal point processes (DPP for short) are investigated. It is shown how to estimate the Kantorovitch–Rubinstein and Wasserstein-2 distances between distributions of DPP. These results are applied to evaluate the accuracy of a fast but approximate simulation algorithm of the Ginibre point process restricted to a circle. One can now simulate in a reasonable amount of time more than ten thousands points.

Investigation of sample paths properties for some classes of φ-sub-Gaussian stochastic processes

Olha Hopkalo Lyudmyla Sakhno

https://doi.org/10.15559/21-VMSTA171

Pub. online: 26 Jan 2021 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications

Abstract

This paper investigates sample paths properties of φ-sub-Gaussian processes by means of entropy methods. Basing on a particular entropy integral, we treat the questions on continuity and the rate of growth of sample paths. The obtained results are then used to investigate the sample paths properties for a particular class of φ-sub-Gaussian processes related to the random heat equation. We derive the estimates for the distribution of suprema of such processes and evaluate their rate of growth.

Logarithmic Lévy process directed by Poisson subordinator

Penka Mayster Assen Tchorbadjieff

https://doi.org/10.15559/19-VMSTA142

Pub. online: 4 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–23

Abstract

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.

Logarithmic Lévy process directed by Poisson subordinator

Penka Mayster Assen Tchorbadjieff

https://doi.org/55.55677/vmsta8878-fine

Pub. online: 4 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–23

Abstract

Properties of Poisson processes directed by compound Poisson-Gamma subordinators

Khrystynas Buchaks Lyudmylas Sakhnos

https://doi.org/98.2555/918VMSTA11

Pub. online: 2 May 2019 Type: Discussion

Open Access

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–23

Abstract

In the paper we consider time-changed Poisson processes where the time is expressed by compound Poisson-Gamma subordinators $G(N(t))$ and derive the expressions for their hitting times. We also study the time-changed Poisson processes where the role of time is played by the processes of the form $G(N(t)+at)$ and by the iteration of such processes.

Studies on generalized Yule models

Federico Polito

https://doi.org/10.15559/vmsta0907

Pub. online: 3 Dec 2018 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications (2025): YY2025, pp. 1–15

Abstract

We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure birth processes or a critical birth-death process. Further, in specific cases we derive the explicit form of the distribution of the number of species of a genus chosen uniformly at random for each time. Besides, we introduce a time-changed mixed Poisson process with the same marginal distribution as that of the time-fractional Poisson process.

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