Detail publikace

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

BAŠTINEC, J. KLIMEŠOVÁ, M.

Originální název

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

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

BAŠTINEC, J.; KLIMEŠOVÁ, M.

Rok RIV

2015

Vydáno

19. 6. 2015

Nakladatel

University of Defence

Místo

Brno

ISBN

978-80-7231-436-2

Kniha

Mathematics, Information Technologies and Applied Sciences 2015

Strany od

8

Strany do

20

Strany počet

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"
}