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On packing dimension preservation by distribution functions of random variables with independent

\tilde{Q}

-digits

Oleksandr Slutskyi

https://doi.org/10.15559/15-VMSTA44

Pub. online: 23 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 371–389

Abstract

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.

On packing dimension preservation by distribution functions of random variables with independent

\tilde{Q}

-digits

Oleksandr Slutskyi

https://doi.org/10.15559/15-MSTA44

Pub. online: 23 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 371–389

Abstract

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.

Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation

Sergii Kuchuk-Iatsenko Yuliya Mishura

https://doi.org/10.15559/15-VMSTA43

Pub. online: 17 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 355–369

Abstract

We consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.

Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation

Sergii Kuchuk-Iatsenko Yuliya Mishura

https://doi.org/10.15559/15-MSTA43

Pub. online: 17 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 355–369

Abstract

Linear regression by observations from mixture with varying concentrations

Daryna Liubashenko Rostyslav Maiboroda

https://doi.org/10.15559/15-VMSTA41

Pub. online: 4 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 343–353

Abstract

We consider a finite mixture model with varying mixing probabilities. Linear regression models are assumed for observed variables with coefficients depending on the mixture component the observed subject belongs to. A modification of the least-squares estimator is proposed for estimation of the regression coefficients. Consistency and asymptotic normality of the estimates is demonstrated.

Linear regression by observations from mixture with varying concentrations

Daryna Liubashenko Rostyslav Maiboroda

https://doi.org/10.15559/15-MSTA41

Pub. online: 4 Dec 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 343–353

Abstract

Extreme residuals in regression model. Minimax approach

Aleksander Ivanov Ivan Matsak Sergiy Polotskiy

https://doi.org/10.15559/15-VMSTA40CNF

Pub. online: 5 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 297–308

Abstract

We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.

Extreme residuals in regression model. Minimax approach

Aleksander Ivanov Ivan Matsak Sergiy Polotskiy

https://doi.org/10.15559/15-MSTA40CNF

Pub. online: 5 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 297–308

Abstract

We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-VMSTA39CNF

Pub. online: 2 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 287–295

Abstract

We show that every multiparameter Gaussian process with integrable variance function admits a Wiener integral representation of Fredholm type with respect to the Brownian sheet. The Fredholm kernel in the representation can be constructed as the unique symmetric square root of the covariance. We analyze the equivalence of multiparameter Gaussian processes by using the Fredholm representation and show how to construct series expansions for multiparameter Gaussian processes by using the Fredholm kernel.

Fredholm representation of multiparameter Gaussian processes with applications to equivalence in law and series expansions

Tommi Sottinen Lauri Viitasaari

https://doi.org/10.15559/15-MSTA39CNF

Pub. online: 2 Oct 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 287–295

Abstract

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