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A multiplicative wavelet-based model for simulation of a random process

Ievgen Turchyn

https://doi.org/10.15559/15-VMSTA33

Pub. online: 24 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 4 (2015), pp. 309–325

Abstract

We find a multiplicative wavelet-based representation for stochastic processes that can be represented as the exponent of a second-order centered random process. We propose a wavelet-based model for simulation of such a stochastic process and find its rates of convergence to the process in different functional spaces in terms of approximation with given accuracy and reliability. This approach allows us to simulate stochastic processes (including certain classes of processes with heavy tails) with given accuracy and reliability.

A multiplicative wavelet-based model for simulation of a random process

Ievgen Turchyn

https://doi.org/10.15559/15-MSTA33

Pub. online: 24 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 4 (2015), pp. 309–325

Abstract

Weak approximation rates for integral functionals of Markov processes

Iurii Ganychenko Alexei Kulik

https://doi.org/10.15559/15-VMSTA37CNF

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 251–266

Abstract

We obtain weak rates for approximation of an integral functional of a Markov process by integral sums. An assumption on the process is formulated only in terms of its transition probability density, and, therefore, our approach is not strongly dependent on the structure of the process. Applications to the estimates of the rates of approximation of the Feynman–Kac semigroup and of the price of “occupation-time options” are provided.

Weak approximation rates for integral functionals of Markov processes

Iurii Ganychenko Alexei Kulik

https://doi.org/10.15559/15-MSTA37CNF

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 251–266

Abstract

Convergence of hitting times for jump-diffusion processes

Georgiy Shevchenko

https://doi.org/10.15559/15-VMSTA32

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 3 (2015): PRESTO-2015, pp. 203–218

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.

Convergence of hitting times for jump-diffusion processes

Georgiy Shevchenko

https://doi.org/10.15559/15-MSTA32

Pub. online: 23 Sep 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 3 (2015): PRESTO-2015, pp. 203–218

Abstract

A group action on increasing sequences of set-indexed Brownian motions

Arthur Yosef

https://doi.org/10.15559/15-VMSTA31

Pub. online: 6 Aug 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 185–198

Abstract

We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projection on all the strictly increasing continuous sequences are one-parameter G-time-changed Brownian motions. In addition, we study the “sequence-independent variation” property for group stationary-increment stochastic processes in general and for a set-indexed Brownian motion in particular. We present some applications.

A group action on increasing sequences of set-indexed Brownian motions

Arthur Yosef

https://doi.org/10.15559/15-MSTA31

Pub. online: 6 Aug 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 185–198

Abstract

A Lundberg-type inequality for an inhomogeneous renewal risk model

Ieva Marija Andrulytė Emilija Bernackaitė Dominyka Kievinaitė Jonas Šiaulys

https://doi.org/10.15559/15-VMSTA30

Pub. online: 31 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 2, Issue 2 (2015), pp. 173–184

Abstract

We obtain a Lundberg-type inequality in the case of an inhomogeneous renewal risk model. We consider the model with independent, but not necessarily identically distributed, claim sizes and the interoccurrence times. In order to prove the main theorem, we first formulate and prove an auxiliary lemma on large values of a sum of random variables asymptotically drifted in the negative direction.

A Lundberg-type inequality for an inhomogeneous renewal risk model

Ieva Marija Andrulytė Emilija Bernackaitė Dominyka Kievinaitė Jonas Šiaulys

https://doi.org/10.15559/15-MSTA30

Pub. online: 31 Jul 2015 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 2, Issue 2 (2015), pp. 173–184

Abstract

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