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Acta Math. Hungar., 121 (3) (2008), 243275. DOI: 10.1007/s10474-008-7117-7
 

Summary: Acta Math. Hungar., 121 (3) (2008), 243275.
DOI: 10.1007/s10474-008-7117-7
First published online September 19, 2008
DISTRIBUTION OF THE MAXIMA
OF RANDOM TAKAGI FUNCTIONS
P. C. ALLAART
Mathematics Department, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430
e-mail: allaart@unt.edu
(Received June 12, 2007; revised April 21, 2008; accepted May 4, 2008)
Abstract. This paper concerns the maximum value and the set of maximum
points of a random version of Takagi's continuous, nowhere dierentiable function.
Let F(x) :=
n=1
1
2
n-1
n(2n-1
x), x R, where 1, 2, . . . are independent,
identically distributed random variables taking values in {-1, 1}, and is the
tent map dened by (x) = 2 dist (x, Z). Let p := P (1 = 1), M := max F(x) :

  

Source: Allaart, Pieter - Department of Mathematics, University of North Texas

 

Collections: Mathematics