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2010 Mathematics Subject Classification index

https://doi.org/10.15559/20-VMSTA74MI

Pub. online: 23 Dec 2020 Type: 2010 Mathematics Subject Classification Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 473–476

Keywords index

https://doi.org/10.15559/20-VMSTA74KI

Pub. online: 23 Dec 2020 Type: Keywords Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 471–472

Author index

https://doi.org/10.15559/20-VMSTA74AI

Pub. online: 23 Dec 2020 Type: Author Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), p. 469

Averaging principle for a stochastic cable equation

Iryna Bodnarchuk

https://doi.org/10.15559/20-VMSTA168

Pub. online: 21 Dec 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 449–467

Abstract

We consider the cable equation in the mild form driven by a general stochastic measure. The averaging principle for the equation is established. The rate of convergence is estimated. The regularity of the mild solution is also studied. The orders in time and space variables in the Holder condition for the solution are improved in comparison with previous results in the literature on this topic.

Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model

Alexander Ivanov

Kateryna Moskvychova

https://doi.org/10.15559/20-VMSTA170

Pub. online: 21 Dec 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 8, Issue 1 (2021), pp. 93–113

Abstract

In a continuous time nonlinear regression model the residual correlogram is considered as an estimator of the stationary Gaussian random noise covariance function. For this estimator the functional central limit theorem is proved in the space of continuous functions. The result obtained shows that the limiting sample continuous Gaussian random process coincides with the limiting process in the central limit theorem for standard correlogram of the random noise in the specified regression model.

Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

Luisa Beghin

Claudio Macci

Barbara Martinucci

https://doi.org/10.15559/20-VMSTA169

Pub. online: 21 Dec 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 8, Issue 1 (2021), pp. 63–91

Abstract

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. This kind of processes are useful in the study of chain molecular diffusions. We give explicit formulas for probability generating functions, and also for means, variances and state probabilities of the random variables of the process. Moreover we study independent random time-changes with the inverse of the stable subordinator, the stable subordinator and the tempered stable subordinator. We also present some asymptotic results in the fashion of large deviations. These results give some generalizations of those presented in [Journal of Statistical Physics 154 (2014), 1352–1364].

Asymptotic normality of modified LS estimator for mixture of nonlinear regressions

Vitalii Miroshnichenko Rostyslav Maiboroda

https://doi.org/10.15559/20-VMSTA167

Pub. online: 8 Dec 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 435–448

Abstract

We consider a mixture with varying concentrations in which each component is described by a nonlinear regression model. A modified least squares estimator is used to estimate the regressions parameters. Asymptotic normality of the derived estimators is demonstrated. This result is applied to confidence sets construction. Performance of the confidence sets is assessed by simulations.

Linear backward stochastic differential equations with Gaussian Volterra processes

Habiba Knani Marco Dozzi

https://doi.org/10.15559/20-VMSTA166

Pub. online: 3 Dec 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 415–433

Abstract

Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional Brownian motion and the multifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a linear second order partial differential equation with terminal condition whose solution is given by a Feynman-Kac type formula.

Subordinated compound Poisson processes of order k

Ayushi Singh Sengar Neelesh S. Upadhye

https://doi.org/10.15559/20-VMSTA165

Pub. online: 5 Nov 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 395–413

Abstract

In this article, the compound Poisson process of order k (CPPoK) is introduced and its properties are discussed. Further, using mixture of tempered stable subordinators (MTSS) and its right continuous inverse, the two subordinated CPPoK with various distributional properties are studied. It is also shown that the space and tempered space fractional versions of CPPoK and PPoK can be obtained, which generalize the process defined in [Statist. Probab. Lett. 82 (2012), 852–858].

On shortfall risk minimization for game options

Yan Dolinsky

https://doi.org/10.15559/20-VMSTA164

Pub. online: 29 Oct 2020 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 7, Issue 4 (2020), pp. 379–394

Abstract

In this paper we study the existence of an optimal hedging strategy for the shortfall risk measure in the game options setup. We consider the continuous time Black–Scholes (BS) model. Our first result says that in the case where the game contingent claim (GCC) can be exercised only on a finite set of times, there exists an optimal strategy. Our second and main result is an example which demonstrates that for the case where the GCC can be stopped on the whole time interval, optimal portfolio strategies need not always exist.

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Online ISSN: 2351-6054
Print ISSN: 2351-6046

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