zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized $n$-Paul paradox. (English) Zbl 1138.60026
The present paper has as starting point the results of S. Csörgö and G. Simons (2002--2006) on the classical St. Petersburg(1/2) game, played by two gamblers with an unbiased coin. The author considers the generalized St. Petersburg($p$) game with $p\in (0, 1)$ as the probability of the “heads” at each throw of a possibly biased coin. An interesting result is that, while the stochastic dominance is preserved for the case of two players and an arbitrary parameter $p\in(0, 1)$, for three or more players, the admissibly pooled winning strategies generally fail to stochastically dominate the individual strategies. The main result of the article consists in determining the best admissible pooling strategies for a rational value of $p$, illustrating also the algebraic depth of the problem for an irrational value of the parameter $p$.

60E99Distribution theory in probability theory
60G50Sums of independent random variables; random walks
Full Text: DOI
[1] Csörgő, S.; Simons, G.: A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games. Statist. probab. Lett. 26, 65-73 (1996) · Zbl 0859.60030
[2] Csörgő, S.; Simons, G.: The two-paul paradox and the comparison of infinite expectations. Limit theorems in probability and statistics, 427-455 (2002) · Zbl 1027.60030
[3] Csörgő, S.; Simons, G.: Laws of large numbers for cooperative St. Petersburg gamblers. Period. math. Hungar. 50, 99-115 (2005) · Zbl 1113.60026
[4] Csörgő, S.; Simons, G.: Pooling strategies for St. Petersburg gamblers. Bernoulli 12, 971-1002 (2006) · Zbl 1130.91018