Euler's approximations of solutions of SDEs with reflecting boundary

For stochastic differential equations reflecting on the boundary of a general convex domain the convergence in Lp and almost surely for recursive projection and discrete penalization schemes are considered. Earlier results by Liu (Ph.D. Thesis, Purdue University), Pettersson (Stochastic Process. Appl. 59(1995)295; Bernoulli 3(4)(1997) 403) and Slominski (Stochastic Process. Appl. 50(1994)197) are generalized and refined. The proofs are based on new estimates for solutions of the Skorokhod problem associated with general semimartingales.