CONTENTS Introduction........................................................................................................5 0. Announcement of results...............................................................................7 1. Condition (UT).............................................................................................18 2. Weak convergence of solutions...................................................................26 3. Convergence in probability..........................................................................35 4. Stability of SDE's with past-dependent and non-Lipschitz coefficients.........43 5. Stability of Stratonovich SDE's.....................................................................49 6. Skorokhod problem, deterministic case........................................................59 7. Skorokhod problem, nondeterministic case..................................................67 8. SDE's with reflecting boundary.....................................................................74 9. Flows of SDE's with reflecting boundary.......................................................83 10. Numerical schemes for SDE's with reflecting boundary..............................87 Appendix A. Convergence in the Skorokhod topology J₁...............................103 Appendix B. (UT) and convergence of stochastic integrals............................106 Appendix C. Gronwall's lemma.......................................................................106 References....................................................................................................108 Index of symbols.............................................................................................112 Index of terms.................................................................................................113
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