內容簡介
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.
圖書目錄
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
