cp's OEIS Frontend

A146206 Number of paths of the simple random walk on condition that the median applied to the partial sums S_0=0, S_1,...,S_n, n odd (n=15 in this example), is equal to integer values k, -[n/2]<=k<=[n/2].

%I A146206 #6 Feb 22 2015 23:28:06
%S A146206 35,91,357,721,1575,2535,3985,5210,3985,2535,1575,721,357,91,35
%N A146206 Number of paths of the simple random walk on condition that the median applied to the partial sums S_0=0, S_1,...,S_n, n odd (n=15 in this example), is equal to integer values k, -[n/2]<=k<=[n/2].
%C A146206 1) A146207=A146205+(0,A146206), see lemma 2 in Pfeifer (2010).
%C A146206 2) The median taken on partial sums of the simple random walk represents the market price in a simulation model wherein a single security among non-cooperating and asymetrically informed traders is traded (Pfeifer et al. 2009).
%D A146206 Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk. Submitted to Stochastic Analysis and Applications.
%H A146206 C. Pfeifer, K. Schredelseker, G. U. H. Seeber, <a href="http://dx.doi.org/10.1016/j.ejor.2008.01.015">On the negative value of information in informationally inefficient markets. Calculations for large number of traders</a>, Eur. J. Operat. Res., 195 (1) (2009) 117-126.
%e A146206 All possible different paths (sequences of partial sums) in case of n=3:
%e A146206 {0,-1,-2,-3}; median=-1.5
%e A146206 {0,-1,-2,-1}; median=-1
%e A146206 {0,-1,0,-1}; median=-0.5
%e A146206 {0,-1,0,1}; median=0
%e A146206 {0,1,0,-1}; median=0
%e A146206 {0,1,0,1}; median=0.5
%e A146206 {0,1,2,1}; median=1
%e A146206 {0,1,2,3}; median=1.5
%e A146206 sequence of integers in case of n=3: 1,2,1
%Y A146206 Cf. A137272, A146205, A146207.
%K A146206 fini,full,nonn
%O A146206 0,1
%A A146206 Christian Pfeifer (christian.pfeifer(AT)uibk.ac.at), Oct 28 2008, May 04 2010
%E A146206 Keyword:full added by _R. J. Mathar_, Sep 17 2009