WIAS Preprint No. 401, (1998)

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.

Appeared in

  • Markov Processes and Related Fields, 6 (2000), no. 3, pp.371-395

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