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Estimates for distribution of suprema of solutions to higher-order partial differential equations with random initial conditions

Yuriy Kozachenko Enzo Orsingher Lyudmyla Sakhno Olga Vasylyk

https://doi.org/10.15559/19-MSTA146

Pub. online: 17 Dec 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 7, Issue 1 (2020), pp. 79–96

Abstract

In the paper we consider higher-order partial differential equations from the class of linear dispersive equations. We investigate solutions to these equations subject to random initial conditions given by harmonizable φ-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema for solutions. We present the examples of processes for which the assumptions of the general result are verified and bounds are written in the explicit form. The main result is also specified for the case of Gaussian initial condition.

Subject index

https://doi.org/10.15559/19-VMSTA64SI

Pub. online: 12 Dec 2019 Type: Subject Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 523–527

Subject index

https://doi.org/10.15559/19-MSTA64SI

Pub. online: 12 Dec 2019 Type: Subject Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 523–527

2010 Mathematics Subject Classification index

https://doi.org/10.15559/19-VMSTA64MI

Pub. online: 12 Dec 2019 Type: 2010 Mathematics Subject Classification Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 519–522

2010 Mathematics Subject Classification index

https://doi.org/10.15559/19-MSTA64MI

Pub. online: 12 Dec 2019 Type: 2010 Mathematics Subject Classification Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 519–522

Keywords index

https://doi.org/10.15559/19-VMSTA64KI

Pub. online: 12 Dec 2019 Type: Keywords Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 517–518

Keywords index

https://doi.org/10.15559/19-MSTA64KI

Pub. online: 12 Dec 2019 Type: Keywords Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), pp. 517–518

Author index

https://doi.org/10.15559/19-VMSTA64AI

Pub. online: 12 Dec 2019 Type: Author Index

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), p. 515

Author index

https://doi.org/10.15559/19-MSTA64AI

Pub. online: 12 Dec 2019 Type: Author Index

Open Access

Journal: Modern Stochastics: Theory and Applications* Volume 6, Issue 4 (2019), p. 515

Jackknife covariance matrix estimation for observations from mixture

Rostyslav Maiboroda Olena Sugakova

https://doi.org/10.15559/19-VMSTA145

Pub. online: 7 Nov 2019 Type: Research Article

Open Access

Journal: Modern Stochastics: Theory and Applications Volume 6, Issue 4 (2019), pp. 495–513

Abstract

A general jackknife estimator for the asymptotic covariance of moment estimators is considered in the case when the sample is taken from a mixture with varying concentrations of components. Consistency of the estimator is demonstrated. A fast algorithm for its calculation is described. The estimator is applied to construction of confidence sets for regression parameters in the linear regression with errors in variables. An application to sociological data analysis is considered.

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