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Subject index

https://doi.org/10.15559/18-VMSTA54SI

Pub. online: 14 Jan 2019 Type: Subject Index

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 551–559

2010 Mathematics Subject Classification index

https://doi.org/10.15559/18-VMSTA54MI

Pub. online: 14 Jan 2019 Type: 2010 Mathematics Subject Classification Index

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 547–550

Keywords index

https://doi.org/10.15559/18-VMSTA54KI

Pub. online: 14 Jan 2019 Type: Keywords Index

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 545–546

Author index

https://doi.org/10.15559/18-VMSTA54AI

Pub. online: 14 Jan 2019 Type: Author Index

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 543–544

Publisher’s word

https://doi.org/10.15559/18-VMSTA54EDI

Pub. online: 14 Jan 2019 Type: Editorial

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 413–414

Editorial

K. Kubilius Yu. Mishura L. Sakhno

https://doi.org/10.15559/18-VMSTA128

Pub. online: 14 Jan 2019 Type: Editorial

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 5, Issue 4 (2018), pp. 411–412

Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields

Davide Giraudo

https://doi.org/10.15559/18-VMSTA121

Pub. online: 21 Dec 2018 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 2 (2019), pp. 251–267

Abstract

Moment inequalities for a class of functionals of i.i.d. random fields are proved. Then rates are derived in the central limit theorem for weighted sums of such randoms fields via an approximation by m-dependent random fields.

Fractional Cox–Ingersoll–Ross process with small Hurst indices

Yuliya Mishura Anton Yurchenko-Tytarenko

https://doi.org/10.15559/18-VMSTA126

Pub. online: 21 Dec 2018 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 1 (2019), pp. 13–39

Abstract

In this paper the fractional Cox–Ingersoll–Ross process on ${\mathbb{R}_{+}}$ for $H<1/2$ is defined as a square of a pointwise limit of the processes ${Y_{\varepsilon }}$, satisfying the SDE of the form $d{Y_{\varepsilon }}(t)=(\frac{k}{{Y_{\varepsilon }}(t){1_{\{{Y_{\varepsilon }}(t)>0\}}}+\varepsilon }-a{Y_{\varepsilon }}(t))dt+\sigma d{B^{H}}(t)$, as $\varepsilon \downarrow 0$. Properties of such limit process are considered. SDE for both the limit process and the fractional Cox–Ingersoll–Ross process are obtained.

Probability distributions for the run-and-tumble models with variable speed and tumbling rate

Luca Angelani Roberto Garra

https://doi.org/10.15559/18-VMSTA127

Pub. online: 21 Dec 2018 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 1 (2019), pp. 3–12

Abstract

In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed according to a non-stationary Poisson distribution with rate $\lambda (t)$. We show that, under suitable assumptions, we are able to find the exact form of the probability distribution. We also consider the space-fractional counterpart of this model, finding the characteristic function of the related process. A conclusive discussion is devoted to the potential applications to run-and-tumble models.

Existence and uniqueness of mild solution to fractional stochastic heat equation

Kostiantyn Ralchenko Georgiy Shevchenko

https://doi.org/10.15559/18-VMSTA122

Pub. online: 12 Dec 2018 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 1 (2019), pp. 57–79

Abstract

For a class of non-autonomous parabolic stochastic partial differential equations defined on a bounded open subset $D\subset {\mathbb{R}^{d}}$ and driven by an ${L^{2}}(D)$-valued fractional Brownian motion with the Hurst index $H>1/2$, a new result on existence and uniqueness of a mild solution is established. Compared to the existing results, the uniqueness in a fully nonlinear case is shown, not assuming the coefficient in front of the noise to be affine. Additionally, the existence of moments for the solution is established.

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

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