## Advanced Topics in Mathematical Logic (V5A6)

### Nonstandard Analysis

### Lecturer

- Dr. Bernhard Irrgang

### Time and location

Wednesdays, 16 - 18, (SR B)Thursdays, 16 - 18, (SR B)

### Contents

The lecture course provides an introduction into Nonstandard Analysis and its applications in stochastics. Nonstandard Analysis is Analyis with infinitesimals, i.e. infinitely small numbers. This approach makes it possible to define notions like limit, continuity and derivative in an alternative, often more intuitive way. It was introduced by A. Robinson in the 1960's.### Skript

### References

- S. Albeverio, J.-E. Fenstadt, R. Hoegh-Krohn, T. Lindström (1986): Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, New York
- D. Landers, L. Rogge (1994): Nichtstandard Analysis, Springer, Berlin
- T. Lindström (1988): An invitation to nonstandard analysis, in Nonstandard Analysis and its Applications, edited by N. Cutland
- S.-A. Ng (2003): Hypermodels in Mathematical Finance, World Scientific, Singapore
- A. Robinson (1966): Nonstandard Analysis, North-Holland, Amsterdam