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Testing proportional hazards for specified covariates

Vilijandas Bagdonavičius Rūta Levulienė

https://doi.org/10.15559/19-VMSTA129

Pub. online: 15 Feb 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 2 (2019), pp. 209–225

Abstract

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data may be right censored. The limit distribution of the test statistic is derived. Power of the test against approaching alternatives is given. Real data examples are considered.

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.

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

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