# On the Stability of a Linear System of Difference Equations with Random Parameters

## Abstract

We study the asymptotic behavior of solutions to a linear system of difference equation whose right-hand side at each time moment depends not only on the value at the previous moment, but also on a random parameter that takes its values in a given set. We obtain conditions of the Lyapunov stability and the asymptotic stability of the equilibrium position that are valid for all values of the random parameter or with probability 1.

- Authors:

- Udmurt State University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771272

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 5; Conference: International symposium on differential equations, Perm (Russian Federation), 17-18 May 2016; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ASYMPTOTIC SOLUTIONS; EQUATIONS; LYAPUNOV METHOD; PROBABILITY; RANDOMNESS; STABILITY

### Citation Formats

```
Rodina, L. I., E-mail: LRodina67@mail.ru.
```*On the Stability of a Linear System of Difference Equations with Random Parameters*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3784-2.

```
Rodina, L. I., E-mail: LRodina67@mail.ru.
```*On the Stability of a Linear System of Difference Equations with Random Parameters*. United States. doi:10.1007/S10958-018-3784-2.

```
Rodina, L. I., E-mail: LRodina67@mail.ru. Tue .
"On the Stability of a Linear System of Difference Equations with Random Parameters". United States. doi:10.1007/S10958-018-3784-2.
```

```
@article{osti_22771272,
```

title = {On the Stability of a Linear System of Difference Equations with Random Parameters},

author = {Rodina, L. I., E-mail: LRodina67@mail.ru},

abstractNote = {We study the asymptotic behavior of solutions to a linear system of difference equation whose right-hand side at each time moment depends not only on the value at the previous moment, but also on a random parameter that takes its values in a given set. We obtain conditions of the Lyapunov stability and the asymptotic stability of the equilibrium position that are valid for all values of the random parameter or with probability 1.},

doi = {10.1007/S10958-018-3784-2},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 5,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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