cp's OEIS Frontend

A146205 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 half-integer values k+1/2, -[n/2]-1<=k<=[n/2].

%I A146205 #2 Jun 01 2010 03:00:00
%S A146205 35,35,245,245,735,735,1225,1225,1225,1225,735,735,245,245,35,35
%N A146205 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 half-integer values k+1/2, -[n/2]-1<=k<=[n/2].
%C A146205 1) Closed-form expressions for sequences see Pfeifer (2010).
%C A146205 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).
%C A146205 3) A146207=A146205+(0,A146206) see lemma 2 in Pfeifer (2010).
%D A146205 Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk, Submitted to Stochastic Analysis and Applications
%H A146205 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 A146205 All possible different paths (sequences of partial sums) in case of n=3:
%e A146205 {0,-1,-2,-3}; median=-1.5
%e A146205 {0,-1,-2,-1}; median=-1
%e A146205 {0,-1,0,-1}; median=-0.5
%e A146205 {0,-1,0,1}; median=0
%e A146205 {0,1,0,-1}; median=0
%e A146205 {0,1,0,1}; median=0.5
%e A146205 {0,1,2,1}; median=1
%e A146205 {0,1,2,3}; median=1.5
%e A146205 sequence of integers in case of n=3: 1,1,1,1
%Y A146205 A117692, A108347, A029460, A029466, A135553, A137272, A146206, A146207
%K A146205 fini,nonn
%O A146205 0,1
%A A146205 Christian Pfeifer (christian.pfeifer(AT)uibk.ac.at), Oct 28 2008, May 04 2010