擴(kuò)散 馬爾可夫過程和鞅 第2卷

內(nèi)容概要

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.

書籍目錄

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 FORMULACHATPER 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 DIFFUSIONSCHAPTER 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 THEORYREFERENCESINDEX

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