Publication detail

Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

BAŠTINEC, J. KLIMEŠOVÁ, M.

Original Title

Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion

Type

conference paper

Language

English

Original Abstract

The natural world is influenced by stochasticity therefore stochastic models are used to test various situations because only the stochastic model can approximate the real model. For example, the stochastic model is used in population, epidemic and genetic simulations in medicine and biology, for simulations in physical and technical sciences, for analysis in economy, financial mathematics, etc. The crucial characteristic of the stochastic model is its stability. This article studies the fundamental theory of the stochastic stability. There is investigated the stability of the solution of stochastic differential equations (SDEs) and systems of SDEs. The article begins with a summary of the stochastic theory. Then, there are inferred conditions for the asymptotic mean square stability of the zero solution of stochastic equation with one-dimensional Brownian motion and system with two-dimensional Brownian motion. There is used a Lyapunov function for proofs of main results.

Keywords

Brownian motion, stochastic differential equation, Lyapunov function, stochastic Lyapunov function, stability, stochastic stability

Authors

BAŠTINEC, J.; KLIMEŠOVÁ, M.

RIV year

2015

Released

19. 6. 2015

Publisher

University of Defence

Location

Brno

ISBN

978-80-7231-436-2

Book

Mathematics, Information Technologies and Applied Sciences 2015

Pages from

8

Pages to

20

Pages count

14

BibTex

@inproceedings{BUT120427,
  author="Marie {Klimešová} and Jaromír {Baštinec}",
  title="Stability of the Zero Solution of Stochastic Differential Systems with Two-dimensional Brownian motion",
  booktitle="Mathematics, Information Technologies and Applied Sciences 2015",
  year="2015",
  pages="8--20",
  publisher="University of Defence",
  address="Brno",
  isbn="978-80-7231-436-2"
}