List of journals
Browse subjects
About Publisher
Help
Sitemap

Home
Search

VTeX: Solutions for Science Publishing

Detailed search

Journals

Title

Author

Types

Abstract

Keywords

Published

Pages

Volumes

Issues

DOI

Affiliation

Classifications

Search results 419

Order by:

Select: All None Download:

Fast

L_{2}

-approximation of integral-type functionals of Markov processes

Iurii Ganychenko

https://doi.org/10.15559/15-VMSTA29

Pub. online: 28 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 165–171

Abstract

In this paper, we provide strong $∈_{8}$-rates of approximation of the integral-type functionals of Markov $w ∈ R$ processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its transition probability density, we get the accuracy that coincides with that obtained in [3] for a one-dimensional diffusion process.

Fast

L_{2}

-approximation of integral-type functionals of Markov processes

Iurii Ganychenko

https://doi.org/10.15559/15-MSTA29

Pub. online: 28 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 165–171

Abstract

In this paper, we provide strong $L_{2}$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its transition probability density, we get the accuracy that coincides with that obtained in [3] for a one-dimensional diffusion process.

Construction of maximum likelihood estimator in the mixed fractional–fractional Brownian motion model with double long-range dependence

Yuliya Mishura Ivan Voronov

https://doi.org/10.15559/15-VMSTA28

Pub. online: 20 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 147–164

Abstract

We construct an estimator of the unknown drift parameter $\theta \in \mathbb{R}$ in the linear model

\[X_{t}=\theta t+\sigma _{1}{B}^{H_{1}}(t)+\sigma _{2}{B}^{H_{2}}(t),\hspace{0.2778em}t\in [0,T],\]

where ${B}^{H_{1}}$ and ${B}^{H_{2}}$ are two independent fractional Brownian motions with Hurst indices $H_{1}$ and $H_{2}$ satisfying the condition $\frac{1}{2}\le H_{1}<H_{2}<1$. Actually, we reduce the problem to the solution of the integral Fredholm equation of the 2nd kind with a specific weakly singular kernel depending on two power exponents. It is proved that the kernel can be presented as the product of a bounded continuous multiplier and weak singular one, and this representation allows us to prove the compactness of the corresponding integral operator. This, in turn, allows us to establish an existence–uniqueness result for the sequence of the equations on the increasing intervals, to construct accordingly a sequence of statistical estimators, and to establish asymptotic consistency.

Construction of maximum likelihood estimator in the mixed fractional–fractional Brownian motion model with double long-range dependence

Yuliya Mishura Ivan Voronov

https://doi.org/10.15559/15-MSTA28

Pub. online: 20 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 147–164

Abstract

We construct an estimator of the unknown drift parameter $\theta \in \mathbb{R}$ in the linear model

\[X_{t}=\theta t+\sigma _{1}{B}^{H_{1}}(t)+\sigma _{2}{B}^{H_{2}}(t),\hspace{0.2778em}t\in [0,T],\]

Identifiability of logistic regression with homoscedastic error: Berkson model

Sergiy Shklyar

https://doi.org/10.15559/15-VMSTA27

Pub. online: 7 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 131–146

Abstract

We consider the Berkson model of logistic regression with Gaussian and homoscedastic error in regressor. The measurement error variance can be either known or unknown. We deal with both functional and structural cases. Sufficient conditions for identifiability of regression coefficients are presented.

Conditions for identifiability of the model are studied. In the case where the error variance is known, the regression parameters are identifiable if the distribution of the observed regressor is not concentrated at a single point. In the case where the error variance is not known, the regression parameters are identifiable if the distribution of the observed regressor is not concentrated at three (or less) points.

The key analytic tools are relations between the smoothed logistic distribution function and its derivatives.

Identifiability of logistic regression with homoscedastic error: Berkson model

Sergiy Shklyar

https://doi.org/10.15559/15-MSTA27

Pub. online: 7 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 131–146

Abstract

The key analytic tools are relations between the smoothed logistic distribution function and its derivatives.

On the Feynman–Kac semigroup for some Markov processes

Victoria Knopova

https://doi.org/10.15559/15-VMSTA26

Pub. online: 18 Jun 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 107–129

Abstract

For a (non-symmetric) strong Markov process X, consider the Feynman–Kac semigroup

\[{T_{t}^{A}}f(x):={\mathbb{E}}^{x}\big[{e}^{A_{t}}f(X_{t})\big],\hspace{1em}x\in {\mathbb{R}}^{n},\hspace{2.5pt}t>0,\]

where A is a continuous additive functional of X associated with some signed measure. Under the assumption that X admits a transition probability density that possesses upper and lower bounds of certain type, we show that the kernel corresponding to ${T_{t}^{A}}$ possesses the density ${p_{t}^{A}}(x,y)$ with respect to the Lebesgue measure and construct upper and lower bounds for ${p_{t}^{A}}(x,y)$. Some examples are provided.

On the Feynman–Kac semigroup for some Markov processes

Victoria Knopova

https://doi.org/10.15559/15-MSTA26

Pub. online: 18 Jun 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 107–129

Abstract

For a (non-symmetric) strong Markov process X, consider the Feynman–Kac semigroup

\[{T_{t}^{A}}f(x):={\mathbb{E}}^{x}\big[{e}^{A_{t}}f(X_{t})\big],\hspace{1em}x\in {\mathbb{R}}^{n},\hspace{2.5pt}t>0,\]

Autoregressive approaches to import–export time series II: a concrete case study

Luca Di Persio Chiara Segala

https://doi.org/10.15559/15-VMSTA25

Pub. online: 1 Jun 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 1 (2015), pp. 67–93

Abstract

The present work constitutes the second part of a two-paper project that, in particular, deals with an in-depth study of effective techniques used in econometrics in order to make accurate forecasts in the concrete framework of one of the major economies of the most productive Italian area, namely the province of Verona. It is worth mentioning that this region is indubitably recognized as the core of the commercial engine of the whole Italian country. This is why our analysis has a concrete impact; it is based on real data, and this is also the reason why particular attention has been taken in treating the relevant economical data and in choosing the right methods to manage them to obtain good forecasts. In particular, we develop an approach mainly based on vector autoregression where lagged values of two or more variables are considered, Granger causality, and the stochastic trend approach useful to work with the cointegration phenomenon.

Autoregressive approaches to import–export time series II: a concrete case study

Luca Di Persio Chiara Segala

https://doi.org/10.15559/15-MSTA25

Pub. online: 1 Jun 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 1 (2015), pp. 67–93

Abstract

34 35 36 37 38

Items per page

Export citation

Copy and paste formatted citation

Formatted citation

Placeholder

Citation style

Download citation in file

Export format

Authors

Placeholder

About Publisher