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Taylor’s power law for the N-stars network evolution model

István Fazekas Csaba Noszály Noémi Uzonyi

https://doi.org/10.15559/19-MSTA137

Pub. online: 16 Sep 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 3 (2019), pp. 311–331

Abstract

Taylor’s power law states that the variance function decays as a power law. It is observed for population densities of species in ecology. For random networks another power law, that is, the power law degree distribution is widely studied. In this paper the original Taylor’s power law is considered for random networks. A precise mathematical proof is presented that Taylor’s power law is asymptotically true for the N-stars network evolution model.

The risk model with stochastic premiums and a multi-layer dividend strategy

Olena Ragulina

https://doi.org/10.15559/19-VMSTA136

Pub. online: 28 Aug 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 3 (2019), pp. 285–309

Abstract

The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber–Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Lastly, numerical illustrations for some multi-layer dividend strategies are presented.

The risk model with stochastic premiums and a multi-layer dividend strategy

Olena Ragulina

https://doi.org/10.15559/19-MSTA136

Pub. online: 28 Aug 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 3 (2019), pp. 285–309

Abstract

Arithmetic of (independent) sigma-fields on probability spaces

Matija Vidmar

https://doi.org/10.15559/19-VMSTA135

Pub. online: 20 Jun 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 3 (2019), pp. 269–284

Abstract

This note gathers what is known about, and provides some new results concerning the operations of intersection, of “generated σ-field”, and of “complementation” for (independent) complete σ-fields on probability spaces.

Arithmetic of (independent) sigma-fields on probability spaces

Matija Vidmar

https://doi.org/10.15559/19-MSTA135

Pub. online: 20 Jun 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 3 (2019), pp. 269–284

Abstract

Moderate deviations for a stochastic Burgers equation

Rachid Belfadli Lahcen Boulanba Mohamed Mellouk

https://doi.org/10.15559/19-MSTA134

Pub. online: 16 May 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 2 (2019), pp. 167–193

Abstract

A moderate deviations principle for the law of a stochastic Burgers equation is proved via the weak convergence approach. In addition, some useful estimates toward a central limit theorem are established.

The asymptotic error of chaos expansion approximations for stochastic differential equations

Tony Huschto Mark Podolskij Sebastian Sager

https://doi.org/10.15559/19-MSTA133

Pub. online: 23 Apr 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 2 (2019), pp. 145–165

Abstract

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.

A copula-based bivariate integer-valued autoregressive process with application

Andrius Buteikis Remigijus Leipus

https://doi.org/10.15559/19-VMSTA131

Pub. online: 12 Mar 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 2 (2019), pp. 227–249

Abstract

A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with copula-joint innovations is studied. Different parameter estimation methods are analyzed and compared via Monte Carlo simulations with emphasis on estimation of the copula dependence parameter. An empirical application on defaulted and non-defaulted loan data is carried out using different combinations of copula functions and marginal distribution functions covering the cases where both marginal distributions are from the same family, as well as the case where they are from different distribution families.

A copula-based bivariate integer-valued autoregressive process with application

Andrius Buteikis Remigijus Leipus

https://doi.org/10.15559/19-MSTA130

Pub. online: 12 Mar 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 2 (2019), pp. 227–249

Abstract

A copula-based bivariate integer-valued autoregressive process with application

Andrius Buteikis Remigijus Leipus

https://doi.org/10.15559/19-VMSTA130

Pub. online: 12 Mar 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 2 (2019), pp. 227–249

Abstract

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