Help

Home
Search

Modern Stochastics: Theory and Applications

Submit your article Information Become a Peer-reviewer

Journal home
To appear
Current issue
All issues
More
Journal home To appear Current issue All issues

Detailed search

Title

Author

Types

Abstract

Keywords

Published

Pages

Volumes

Issues

DOI

Affiliation

Classifications

Search results 301

Order by:

Select: All None Download:

Corrigendum to “Asymptotic normality of corrected estimator in Cox proportional hazards model with measurement error”

C. Chimisov A. Kukush

https://doi.org/10.15559/vmsta-2014.13

Pub. online: 13 Nov 2014 Type: Corrigendum

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 127–128

Rates of approximation of nonsmooth integral-type functionals of Markov processes

Iu. Ganychenko A. Kulik

https://doi.org/10.15559/vmsta-2014.12

Pub. online: 15 Sep 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 117–126

Abstract

We provide strong $L_{p}$-rates of approximation of nonsmooth integral-type functionals of Markov processes by integral sums. Our approach is, in a sense, process insensitive and is based on a modification of some well-developed estimates from the theory of continuous additive functionals of Markov processes.

On the distribution of integral functionals of a homogeneous diffusion process

M. Perestyuk Yu. Mishura G. Shevchenko

https://doi.org/10.15559/vmsta-2014.10

Pub. online: 29 Aug 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 109–116

Abstract

In this article, we study homogeneous transient diffusion processes. We provide the basic distributions of their local times. It helps to get exact formulas and upper bounds for the moments, exponential moments, and potentials of integral functionals of transient diffusion processes. Some of the results generalize the corresponding results of Salminen and Yor for the Brownian motion with drift.

European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process

Yu. Mishura G. Rizhniak V. Zubchenko

https://doi.org/10.15559/vmsta-2014.1.1.2

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 95–108

Abstract

European call option issued on a bond governed by a modified geometric Ornstein-Uhlenbeck process, is investigated. Objective price of such option as a function of the mean and the variance of a geometric Ornstein-Uhlenbeck process is studied. It is proved that the “Ornstein-Uhlenbeck” market is arbitrage-free and complete. We obtain risk-neutral measure and calculate the fair price of a call option. We consider also the bond price, governed by a modified fractional geometric Ornstein-Uhlenbeck process with Hurst index $H\in (1/2,1)$. Limit behaviour of the variance of the process as $H\to 1/2$ and $H\to 1$ is studied, the monotonicity of the variance and the objective price of the option as a function of Hurst index is established.

Strong limit theorems for anisotropic self-similar fields

V. Makogin Yu. Mishura

https://doi.org/10.15559/vmsta-2014.1.1.1

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 73–93

Abstract

Our paper starts from presentation and comparison of three definitions for the self-similar field. The interconnection between these definitions has been established. Then we consider the Lamperti scaling transformation for the self-similar field and investigate the connection between the scaling transformation for such field and the shift transformation for the corresponding stationary field. It was also shown that the fractional Brownian sheet has the ergodic scaling transformation. The strong limit theorems for the anisotropic growth of the sample paths of the self-similar field at 0 and at ∞ for the upper and lower functions have been proved. It was obtained the upper bound for growth of the field with ergodic scaling transformation for slowly varying functions. We present some examples of iterated log-type limits for the Gaussian self-similar random fields.

Strong uniqueness of solutions of stochastic differential equations with jumps and non-Lipschitz random coefficients

G. Kulinich S. Kushnirenko

https://doi.org/10.15559/vmsta-2014.1.1.6

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 65–72

Abstract

In the paper we establish strong uniqueness of solution of a system of stochastic differential equations with random non-Lipschitz coefficients that involve both the square integrable continuous vector martingales and centered and non-centered Poisson measures.

Transportation distance between the Lévy measures and stochastic equations for Lévy-type processes

T. Kosenkova A. Kulik

https://doi.org/10.15559/vmsta-2014.1.1.7

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 49–64

Abstract

The notion of the transportation distance on the set of the Lévy measures on $\mathbb{R}$ is introduced. A Lévy-type process with a given symbol (state dependent analogue of the characteristic triplet) is proved to be well defined as a strong solution to a stochastic differential equation (SDE) under the assumption of Lipschitz continuity of the Lévy kernel in the symbol w.r.t. the state space variable in the transportation distance. As examples, we construct Gamma-type process and α-stable like process as strong solutions to SDEs.

LAN property for discretely observed solutions to Lévy driven SDE’s

D. Ivanenko A. Kulik

https://doi.org/10.15559/vmsta-2014.1.1.4

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 33–47

Abstract

The LAN property is proved in the statistical model based on discrete-time observations of a solution to a Lévy driven SDE. The proof is based on a general sufficient condition for a statistical model based on discrete observations of a Markov process to possess the LAN property, and involves substantially the Malliavin calculus-based integral representations for derivatives of log-likelihood of the model.

Asymptotic normality of corrected estimator in Cox proportional hazards model with measurement error

C. Chimisov A. Kukush

https://doi.org/10.15559/vmsta-2014.1.1.3

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 13–32

Abstract

Cox proportional hazards model is considered. In Kukush et al. (2011), Journal of Statistical Research, Vol. 45, No. 2, 77–94 simultaneous estimators $\lambda _{n}(\cdot )$ and $\beta _{n}$ of baseline hazard rate $\lambda (\cdot )$ and regression parameter β are studied. The estimators maximize the objective function that corrects the log-likelihood function for measurement errors and censoring. Parameter sets for $\lambda (\cdot )$ and β are convex compact sets in $C[0,\tau ]$ and ${\mathbb{R}}^{k}$, respectively. In present paper the asymptotic normality for $\beta _{n}$ and linear functionals of $\lambda _{n}(\cdot )$ is shown. The results are valid as well for a model without measurement errors. A way to compute the estimators is discussed based on the fact that $\lambda _{n}(\cdot )$ is a linear spline.

The consistent criteria of hypotheses

L. Aleksidze M. Mumladze Z. Zerakidze

https://doi.org/10.15559/vmsta-2014.1.1.5

Pub. online: 27 Jun 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 1 (2014), pp. 3–11

Abstract

In this paper we define the consistent criteria of hypotheses such as the probability of any kind of errors is zero for given criteria. We prove necessary and sufficient conditions for the existence of such criteria.

28 29 30 31

Items per page

Export citation

Copy and paste formatted citation

Formatted citation

Placeholder

Citation style

Download citation in file

Export format

Authors

Placeholder

RSS

MSTA

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

About

About journal
Indexed in
Editors-in-Chief

For contributors

Submit
OA Policy
Become a Peer-reviewer

Contact us

ejournals-vmsta@vtex.lt
Mokslininkų 2A
LT-08412 Vilnius
Lithuania