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| Some Frequently Used Notation CHAPTER IV. INTRODUCTION TO ITO CALCULUS TERMINOLOGY AND CONVENTIONS R-processes and L-processes Usual conditions， etc. Important convention about time 0 1. SOME MOTIVATING REMARKS 1. Ito integrals 2. Integration by parts 3. Ito‘s formula for Brownian motion 4. A rough plan of the chapter 2. SOME FUNDAMENTAL IDEAS: PREVISIBLE PROCESSES，LOCALIZATION， etc. Previsible processes 5. Basic integrands Z[S， T] 6. Previsible processes on (0， )， b， b Finite-variation and integrable-variation processes 7. FVo and IVo processes 8. Preservation of the martingale property Localization 9. H[O， T]， XT 10.Localization of integrands ib 11.Localizationof integratiors 12.Nil desperandum 13.Extending stochastic integrls by localization 14.Local martinales,and the fatou lemma 15.Semimartingales 16.Integrators Liekeihood ratios 17.Martingale property under change of measure. 3 THE ELEMENTARY THEORY OF FINITE VARIATION PROCESSES 4 STOCHASTIC INTEGRALS:THE THEORY 5 STOCHASTIC INTEGRALS WITH RESPECT TO CONTINUOUS SEMIMARTINGALSE 6 APPLICATIONS OF ITOS FORMULA CHATPER V.STOCHASTIC DIFFERENTIAL EQUATIONS AND DIFFUSIONS 1 INTRODUCTION 2 PATHWISE UNIQUENESS,STRONG SDE AND FLOWS 3 WEAK SOLUTIONS UNIQUENESS IN LAW 4 MARTINGALE PROBLEMS MARKOV PROPERTY 5 OVERTURE TO STOCHASTIC DIFFERENTAL GEOMETRY 6 ONE-DIMENSIONAL SDE 7 ONE-DIMENSIONAL DIFFUSIONS CHAPTER VI.THE GENERAL THEORY 1 ORIENTATION 2 DEBUR AND SECTION THEOREMS 3 OPTIONAL PROJECTIONS AND FILTENING 4 CHARACTERIZING PREVISIBLE TIMES 5 DUAL PREVISIBLE PROJECTIONS 6 THE MEYER DECOMPOSITON THEROM 7 STOCHASTIC INTEGRATION HE GENERAL CASE 8 ITO EXCURSION THEORY REFERENCES INDEX |
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