- Tytuł:
- The law of large numbers and a functional equation
- Autorzy:
- Sablik, Maciej
- Powiązania:
- https://bibliotekanauki.pl/articles/1294499.pdf
- Data publikacji:
- 1998
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
functional equation
law of large numbers
Jensen equation on curves
bounded solutions
difference equation - Opis:
- We deal with the linear functional equation (E) $g(x) = ∑^r_{i=1} p_i g(c_i x)$, where g:(0,∞) → (0,∞) is unknown, $(p₁,...,p_r)$ is a probability distribution, and $c_i$'s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli's Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
- Źródło:
-
Annales Polonici Mathematici; 1998, 68, 2; 165-175
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł