## View abstract

### Session S12 - Delay and functional differential equations and applications

Wednesday, July 21, 17:10 ~ 17:45 UTC-3

## On local stability of stochastic delay nonlinear discrete systems with state-dependent noise

### Alexandra Rodkina

#### The University of the West Indies, Jamaica   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak1f8a8c0d98546bab25d230bec6af9145').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy1f8a8c0d98546bab25d230bec6af9145 = '&#97;l&#101;chk&#97;jm' + '&#64;'; addy1f8a8c0d98546bab25d230bec6af9145 = addy1f8a8c0d98546bab25d230bec6af9145 + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m'; var addy_text1f8a8c0d98546bab25d230bec6af9145 = '&#97;l&#101;chk&#97;jm' + '&#64;' + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m';document.getElementById('cloak1f8a8c0d98546bab25d230bec6af9145').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy1f8a8c0d98546bab25d230bec6af9145 + '\'>'+addy_text1f8a8c0d98546bab25d230bec6af9145+'<\/a>';

We examine the local stability of solutions of a delay stochastic nonlinear difference equation with deterministic and state-dependent Gaussian perturbations. We apply the degenerate Lyapunov-Krasovskii functional technique and construct a sequence of events, each term of which is defined by a bound on a normally distributed random variable. Local stability holds on the intersection of these events, which has probability at least $1-\gamma$, $\gamma\in (0,1)$. This probability can be made arbitrarily high by choosing the initial value sufficiently small. We also present a generalization to systems where a condition for stability is expressed in terms of the diagonal part of the unperturbed system, and computer simulations which illustrate our results.

Joint work with Josef Diblik (Brno University of Technology, Czech Republic) and Zdenek Smarda (Brno University of Technology, Czech Republic).