For more information about this meeting, contact Mari Royer, Yakov Pesin, Anatole Katok, Svetlana Katok, Dmitri Burago.
|Title:||The generalized St. Petersburg games and its applications to p-adic series expansions|
|Seminar:||Center for Dynamics and Geometry Seminar|
|Speaker:||Eveyth Deligero, U South Eastern Philippines|
|The St. Petersburg games is a classical example of an iid sequence of random variables with
inﬁnite expectation and so for a single game the ’fair’ entry fee is not determined. However, if
the game is continuously played, Feller (1948) showed that the weak law of large numbers holds.
Since then several results had been published and Vardi (1997) showed that known results for
continued fraction can be obtained for the classical St. Petersburg games using the same proof
technique. But for the case of the generalized St. Petersburg games, results obtained can be
applied directly to continued fraction and other series expansions of formal Laurent series and to
some series expansions of p-adic numbers.
In this talk, we brieﬂy recall the deﬁnition of St. Petersburg games and discuss some results
obtained for the generalized St. Petersburg games. Then we show its applications to some p-adic
series expansions. In particular, we discuss its applications to Oppenheim expansion which include
Luroth, Engel and Sylvester as particular cases and see if it could be applied to p-adic continued
fraction of Ruban.|
Room Reservation Information
|Date:||03 / 25 / 2009|
|Time:||03:30pm - 05:30pm|