## 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

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.