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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.

Moderate deviations for a stochastic Burgers equation

Rachid Belfadli Lahcen Boulanba Mohamed Mellouk

https://doi.org/10.15559/19-VMSTA134

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-VMSTA133

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-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

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.

Note on AR(1)-characterisation of stationary processes and model fitting

Marko Voutilainen

Lauri Viitasaari Pauliina Ilmonen

https://doi.org/10.15559/19-VMSTA132

Pub. online: 8 Mar 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 2 (2019), pp. 195–207

Abstract

It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form estimators for the model parameter based on autocovariance estimators for several different lags. However, this estimation procedure may fail in some special cases. In this article, a detailed analysis of these special cases is provided. In particular, it is proved that these cases correspond to degenerate processes.

Editorial

K. Kubilius Yu. Mishura L. Sakhno

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

Pub. online: 19 Feb 2019 Type: Editorial

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 1 (2019), pp. 1–2

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