| Creators: |
Grabinski, Michael and Klinkova, Galiya |
| Title: |
Like a Sum Is Generalized into an Integral, a Product May Be Generalized into an Inteduct |
| Item Type: |
Article or issue of a publication series |
| Journal or Series Title: |
Applied Mathematics |
| Page Range: |
pp. 279-289 |
| Additional Information: |
Open Access |
| Date: |
29 April 2023 |
| Divisions: |
Wirtschaftswissenschaften |
| Abstract (ENG): |
It is well known that an integral is nothing but a continuous form of a sum. Is it possible to do the same thing with a product? The answer is yes and done
for the first time in this publication. The new operator is called inteduct. As an integral is a proper tool to calculate the arithmetic mean of a function, the
inteduct gives the geometric mean of a function. This defines a new branch of mathematics. Most applications may lay way ahead. Only some are discussed here. One is applying the inteduct to probability theory. There it is possible
e.g., to determine a function for a life expectation rather than just a numerical value. Another application is to distinguish chaos from randomness within numerically given values. At least for the logistic map there exists a direct connection between Lyapunov exponent and inteduct. To distinguish between chaos and randomness is particularly important in finance. While random ness implies ergodicity, chaos is non-ergodic. And many fundamental financial theories from portfolio theory to market efficiency require ergodicity. |
| Forthcoming: |
No |
| Language: |
English |
| Uncontrolled Keywords: |
Geometric Mean, Chaos, Finance, Ergodicity |
| Link eMedia: |
Download |
| Citation: |
Grabinski, Michael and Klinkova, Galiya
(2023)
Like a Sum Is Generalized into an Integral, a Product May Be Generalized into an Inteduct.
Applied Mathematics, 14 (5).
pp. 279-289.
ISSN 2152-7393
|
 |
View Item in edit mode (academic staff only) |
