#### Results in Journal Modern Stochastics: Theory and Applications: 186

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Oleksandr Slutskyi
Published: 23 December 2015
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Modern Stochastics: Theory and Applications, Volume 2, pp 371-389; doi:10.15559/15-vmsta44

Abstract:
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: On packing dimension preservation by distribution functions of random variables with independent Q˜-digits, Authors: Oleksandr Slutskyi , The article is devoted to finding conditions for the packing dimension preservation by distribution functions of random variables with independent $\tilde{Q}$-digits. The notion of “faithfulness of fine packing systems for packing dimension calculation” is introduced, and connections between this notion and packing dimension preservation are found.
V. Makogin, Yu. Mishura
Published: 17 June 2014
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Modern Stochastics: Theory and Applications, Volume 1, pp 73-93; doi:10.15559/vmsta-2014.1.1.1

Yu. Mishura, G. Rizhniak, V. Zubchenko
Published: 17 June 2014
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Modern Stochastics: Theory and Applications, Volume 1, pp 95-108; doi:10.15559/vmsta-2014.1.1.2

T. Kosenkova, A. Kulik
Published: 17 June 2014
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Modern Stochastics: Theory and Applications, Volume 1, pp 49-64; doi:10.15559/vmsta-2014.1.1.7

Peter Parczewski
Published: 18 September 2017
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Modern Stochastics: Theory and Applications, Volume 4, pp 189-198; doi:10.15559/17-vmsta82

Abstract:
We extend the Poincaré–Borel lemma to a weak approximation of a Brownian motion via simple functionals of uniform distributions on n-spheres in the Skorokhod space $D([0,1])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Csörgő et al. (2003). Some notes on spheres with respect to $\ell_p$-norms are given.
Dmytro Marushkevych
Published: 7 June 2016
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Modern Stochastics: Theory and Applications, Volume 3, pp 107-117; doi:10.15559/16-vmsta54

Abstract:
We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein–Uhlenbeck process driven by mixed fractional Brownian motion.
Svetlana Danilenko, Simona Paškauskaitė, Jonas Šiaulys
Published: 4 April 2016
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Modern Stochastics: Theory and Applications, Volume 3, pp 79-94; doi:10.15559/16-vmsta52

Abstract:
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on $\{\xi_1,\xi_2,\ldots\}$ and~$\eta$ under which the distribution function of the random sum $S_\eta=\xi_1+\xi_2+\cdots+\xi_\eta$ belongs to the class of $\mathcal{O}$-exponential distributions.
Larysa Pryhara, Georgiy Shevchenko
Published: 30 June 2016
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Modern Stochastics: Theory and Applications, Volume 3, pp 133-144; doi:10.15559/16-vmsta56

Abstract:
We consider a Cauchy problem for stochastic heat equation driven by a real harmonizable fractional stable process $Z$ with Hurst parameter $H>1/2$ and stability index $\alpha>1$. It is shown that the approximations for its solution, which are defined by truncating the LePage series for $Z$, converge to the solution.
Georgiy Shevchenko
Published: 23 September 2015
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Modern Stochastics: Theory and Applications, Volume 2; doi:10.15559/15-vmsta32

Abstract:
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the equations and of the moments when the solutions hit certain sets.
Kostiantyn Ralchenko
Published: 13 April 2015
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Modern Stochastics: Theory and Applications, Volume 2, pp 17-28; doi:10.15559/15-vmsta21

Abstract:
We prove the asymptotic normality of the discretized maximum likelihood estimatorfor the drift parameter in the homogeneous ergodic diffusion model.
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