We apologize for the considerable delay in departure.Anyone who knows what has been happening to British universities will need no further explanation, and will share our sadness.(b) The book is meant to help the research student reach the stage where he or she can begin both to think up and tackle new problems and to read the up-to-date literature across a wide spectrum; and to persuade him or her that it is worth the effort.

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.FV0 and IV0 processes

8.Preservation of the martingale property

Localization

9.H[0,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