On approximation of solutions of one-dimensional reflecting SDEs with discontinuous coefficients

For stochastic differential equations reflecting on the boundary of a connected interval in R we discuss the problem of approximation for solutions. The main results are convergence in law as well as in Lp of discrete schemes that fundamentally generalize the classical Euler and Euler–Peano schemes considered in Semrau-Giłka (2013). The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure and the diffusion coefficient may degenerate on some subsets of the domain. New generalized inequalities of Krylov’s type for stochastic integrals are crucial tools used in the proofs.