Description
Book SynopsisUsing only the very elementary framework of finite probability spaces, this book treats a number of topics in the modern theory of stochastic processes. This is made possible by using a small amount of Abraham Robinson's nonstandard analysis and not attempting to convert the results into conventional form.
Table of Contents*Frontmatter, pg. i*Table of contents, pg. v*Preface, pg. vii*Acknowledgments, pg. ix*1. Random variables, pg. 1*2. Algebras of random variables, pg. 6*3. Stochastic processes, pg. 10*4. External concepts, pg. 12*5. Infinitesimals, pg. 16*6. External analogues of internal notions, pg. 20*7. Properties that hold almost everywhere, pg. 25*8. L1 random variables 30, pg. 30*9. The decomposition of a stochastic process, pg. 33*10. The total variation of a process, pg. 37*11. Convergence of martingales, pg. 41*12. Fluctuations of martingales, pg. 48*13. Discontinuities of martingales, pg. 53*14. The Lindeberg condition, pg. 57*15. The maximum of a martingale, pg. 61*16. The law of large numbers, pg. 63*17. Nearly equivalent stochastic processes, pg. 72*18. The de Moivre-Laplace-Lindeberg-Feller-Wiener- Levy-Doob-Erdos-Kac-Donsker-Prokhorov theorem, pg. 75*Appendix, pg. 80*Index, pg. 95
