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Keywords index

https://doi.org/10.15559/19-MSTA64KI

Pub. online: 12 Dec 2019 Type: Keywords Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 517–518

Author index

https://doi.org/10.15559/19-VMSTA64AI

Pub. online: 12 Dec 2019 Type: Author Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), p. 515

Author index

https://doi.org/10.15559/19-MSTA64AI

Pub. online: 12 Dec 2019 Type: Author Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), p. 515

Jackknife covariance matrix estimation for observations from mixture

Rostyslav Maiboroda Olena Sugakova

https://doi.org/10.15559/19-VMSTA145

Pub. online: 7 Nov 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 495–513

Abstract

A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered.

Jackknife covariance matrix estimation for observations from mixture

Rostyslav Maiboroda Olena Sugakova

https://doi.org/10.15559/19-MSTA145

Pub. online: 7 Nov 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 495–513

Abstract

BSDEs and log-utility maximization for Lévy processes

Paolo Di Tella Hans-Jürgen Engelbert

https://doi.org/10.15559/19-VMSTA144

Pub. online: 28 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 479–494

Abstract

In this paper we establish the existence and the uniqueness of the solution of a special class of BSDEs for Lévy processes in the case of a Lipschitz generator of sublinear growth. We then study a related problem of logarithmic utility maximization of the terminal wealth in the filtration generated by an arbitrary Lévy process.

BSDEs and log-utility maximization for Lévy processes

Paolo Di Tella Hans-Jürgen Engelbert

https://doi.org/10.15559/19-MSTA144

Pub. online: 28 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 479–494

Abstract

On a linear functional for infinitely divisible moving average random fields

Stefan Roth

https://doi.org/10.15559/19-VMSTA143

Pub. online: 22 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 443–478

Abstract

Given a low-frequency sample of the infinitely divisible moving average random field $\{{\textstyle\int _{{\mathbb{R}^{d}}}}f(t-x)\Lambda (dx),\hspace{2.5pt}t\in {\mathbb{R}^{d}}\}$, in [13] we proposed an estimator $\widehat{u{v_{0}}}$ for the function $\mathbb{R}\ni x\mapsto u(x){v_{0}}(x)=(u{v_{0}})(x)$, with $u(x)=x$ and ${v_{0}}$ being the Lévy density of the integrator random measure Λ. In this paper, we study asymptotic properties of the linear functional ${L^{2}}(\mathbb{R})\ni v\mapsto {\left\langle v,\widehat{u{v_{0}}}\right\rangle _{{L^{2}}(\mathbb{R})}}$, if the (known) kernel function f has a compact support. We provide conditions that ensure consistency (in mean) and prove a central limit theorem for it.

On a linear functional for infinitely divisible moving average random fields

Stefan Roth

https://doi.org/10.15559/19-MSTA143

Pub. online: 22 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 443–478

Abstract

On estimation of expectation of simultaneous renewal time of time-inhomogeneous Markov chains using dominating sequence

Vitaliy Golomoziy

https://doi.org/10.15559/19-VMSTA138

Pub. online: 14 Oct 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 3 (2019), pp. 333–343

Abstract

The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the specific set C by both processes. Under the condition of existence a dominating sequence for both renewal sequences generated by the chains and non-lattice condition for renewal probabilities an upper bound for the expectation of the simultaneous renewal time is obtained.

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