In 2016 we received a special request to include a report from a renowned mathematician, LAJOS TAKÁCS. His work “THEORY OF RANDOM FLUCTUATIONS” dates from 1973.
In our view it would be a service to the applied probability community if this old manuscript could be made publicly available. The manuscript seems valuable both from a scientific and historic perspective, and contains numerous references.
To make this extensive work available online, we have digitized all chapters, which were originally worked out on a hand-typewriter.
We are grateful to Mrs. Dalma Takács for making the manuscript available to us. We further refer to “Queueing Systems” for an obituary of Lajos Takács, who died in December 2015.
Below you will find the links to all the chapters of the book:
Note: the pdf search function (controle-F) has been enabled in these files
i. Preface, Contents, Introduction, Typographical details
1. BASIC THEORY
2. MAXIMAL PARTIAL SUMS
3. POSITIVE PARTIAL SUMS
4. ORDERED PARTIAL SUMS
5. RANDOM WALKS, BALLOT THEOREMS AND ORDER STATISTICS
6. LIMIT THEOREMS FOR SUMS OF INDEPENDENT RANDOM VARIABLES
7. STOCHASTIC PROCESSES
8. THE DISTRIBUTION OF THE SUPREMUM FOR STOCHASTIC PROCESSES
9. OCCUPATION TIME PROBLEMS
10. QUEUEING, RISK AND STORAGE PROBLEMS
ii. Appendix
iii. Solutions