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On fractal faithfulness and fine fractal properties of random variables with independent

Q^{*}

-digits

Muslem Ibragim Grygoriy Torbin

https://doi.org/10.15559/16-VMSTA55

Pub. online: 9 Jun 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), pp. 119–131

Abstract

We develop a new technique to prove the faithfulness of the Hausdorff–Besicovitch dimension calculation of the family $\varPhi ({Q}^{\ast })$ of cylinders generated by ${Q}^{\ast }$-expansion of real numbers. All known sufficient conditions for the family $\varPhi ({Q}^{\ast })$ to be faithful for the Hausdorff–Besicovitch dimension calculation use different restrictions on entries $q_{0k}$ and $q_{(s-1)k}$. We show that these restrictions are of purely technical nature and can be removed. Based on these new results, we study fine fractal properties of random variables with independent ${Q}^{\ast }$-digits.

On fractal faithfulness and fine fractal properties of random variables with independent

Q^{*}

-digits

Muslem Ibragim Grygoriy Torbin

https://doi.org/10.15559/16-MSTA55

Pub. online: 9 Jun 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), pp. 119–131

Abstract

Large deviations for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process

Dmytro Marushkevych

https://doi.org/10.15559/16-VMSTA54

Pub. online: 7 Jun 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), pp. 107–117

Abstract

We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein–Uhlenbeck process driven by mixed fractional Brownian motion.

Large deviations for drift parameter estimator of mixed fractional Ornstein–Uhlenbeck process

Dmytro Marushkevych

https://doi.org/10.15559/16-MSTA54

Pub. online: 7 Jun 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), pp. 107–117

Abstract

We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein–Uhlenbeck process driven by mixed fractional Brownian motion.

Erratum to “Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

”

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-VMSTA53

Pub. online: 16 May 2016 Type: Erratum

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 2 (2016), p. 105

Erratum to “Asymptotic normality of total least squares estimator in a multivariate errors-in-variables model

A X = B

”

Alexander Kukush Yaroslav Tsaregorodtsev

https://doi.org/10.15559/16-MSTA53

Pub. online: 16 May 2016 Type: Erratum

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 2 (2016), p. 105

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-VMSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Asymptotics of exponential moments of a weighted local time of a Brownian motion with small variance

Alexei Kulik Daryna Sobolieva

https://doi.org/10.15559/16-MSTA49

Pub. online: 5 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 95–103

Abstract

We prove a large deviation type estimate for the asymptotic behavior of a weighted local time of $\varepsilon W$ as $\varepsilon \to 0$.

Random convolution of inhomogeneous distributions with

O

-exponential tail

Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys

https://doi.org/10.15559/16-VMSTA52

Pub. online: 4 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 3, Issue 1 (2016), pp. 79–94

Abstract

Let $\{\xi _{1},\xi _{2},\dots \}$ be a sequence of independent random variables (not necessarily identically distributed), and η be a counting random variable independent of this sequence. We obtain sufficient conditions on $\{\xi _{1},\xi _{2},\dots \}$ and η 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.

Random convolution of inhomogeneous distributions with

O

-exponential tail

Svetlana Danilenko Simona Paškauskaitė Jonas Šiaulys

https://doi.org/10.15559/16-MSTA52

Pub. online: 4 Apr 2016 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 3, Issue 1 (2016), pp. 79–94

Abstract

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