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A criterion for testing hypotheses about the covariance function of a stationary Gaussian stochastic process

Yuriy Kozachenko Viktor Troshki

https://doi.org/10.15559/15-MSTA17

Pub. online: 29 Jan 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 1, Issue 2 (2014), pp. 139–149

Abstract

We consider a measurable stationary Gaussian stochastic process. A criterion for testing hypotheses about the covariance function of such a process using estimates for its norm in the space $L_{p}(\mathbb{T})$, $p\ge 1$, is constructed.

Heat equation with general stochastic measure colored in time

Vadym Radchenko

https://doi.org/10.15559/14-VMSTA14

Pub. online: 5 Dec 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 1, Issue 2 (2014), pp. 129–138

Abstract

A stochastic heat equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure $d\mu (t)$ is investigated in this paper. For the integrator μ, we assume the σ-additivity in probability only. The existence, uniqueness, and Hölder regularity of the solution are proved.

Heat equation with general stochastic measure colored in time

Vadym Radchenko

https://doi.org/10.15559/14-MSTA14

Pub. online: 5 Dec 2014 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 1, Issue 2 (2014), pp. 129–138

Abstract

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

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

C. Chimisov A. Kukush

https://doi.org/10.15559/MSTA-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.

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

Iu. Ganychenko A. Kulik

https://doi.org/10.15559/MSTA-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

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.

On the distribution of integral functionals of a homogeneous diffusion process

M. Perestyuk Yu. Mishura G. Shevchenko

https://doi.org/10.15559/MSTA-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

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.

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