On deterministic and stochastic sliding modes via small diffusion approximation
- Milstein, Grigori N.
- Veretennikov, Alexandre Yu.
2010 Mathematics Subject Classification
- 34A60 60H10
- Differential equations with discontinuous right-hand sides, sliding modes, stochastic differential equations, stochastic averaging principle, stochastic differential equations with small noise
We study solutions of a system of ordinary differential equations with discontinuity of its vector field on a smooth surface via small additive diffusion perturbations. When a diffusion term tends to zero, one obtains limiting sliding modes on the surface with explicit representation for its motion law. Stochastic sliding modes are also established.
- Markov Processes and Related Fields, 6 (2000), no. 3, pp.371-395