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