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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]. 4

%I #6 Feb 22 2015 23:28:06

%S 35,91,357,721,1575,2535,3985,5210,3985,2535,1575,721,357,91,35

%N 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 1) A146207=A146205+(0,A146206), see lemma 2 in Pfeifer (2010).

%C 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 Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk. Submitted to Stochastic Analysis and Applications.

%H 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 All possible different paths (sequences of partial sums) in case of n=3:

%e {0,-1,-2,-3}; median=-1.5

%e {0,-1,-2,-1}; median=-1

%e {0,-1,0,-1}; median=-0.5

%e {0,-1,0,1}; median=0

%e {0,1,0,-1}; median=0

%e {0,1,0,1}; median=0.5

%e {0,1,2,1}; median=1

%e {0,1,2,3}; median=1.5

%e sequence of integers in case of n=3: 1,2,1

%Y Cf. A137272, A146205, A146207.

%K fini,full,nonn

%O 0,1

%A Christian Pfeifer (christian.pfeifer(AT)uibk.ac.at), Oct 28 2008, May 04 2010

%E Keyword:full added by _R. J. Mathar_, Sep 17 2009

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