Euler's approximations of solutions of SDEs with reflecting boundary

For stochastic differential equations reflecting on the boundary of a gener al convex domain the convergence in L-P and almost surely for recursive pro jection and discrete penalization schemes are considered. Earlier results b y Liu (Ph.D. Thesis, Purdue University), Pettersson (Stochastic Process. Ap pl. 59 (1995) 295; Bernoulli 3(4) (1997) 403) and Stominski (Stochastic Pro cess. Appl. 50 (1994) 197) are generalized and refined. The proofs are base d on new estimates for solutions of the Skorokhod problem associated with g eneral semimartingales. (C) 2001 Elsevier Science B.V. All rights reserved.