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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]. 4
35, 35, 245, 245, 735, 735, 1225, 1225, 1225, 1225, 735, 735, 245, 245, 35, 35 (list; graph; refs; listen; history; text; internal format)
1) Closed-form expressions for sequences see Pfeifer (2010).
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).
3) A146207=A146205+(0,A146206) see lemma 2 in Pfeifer (2010).
Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk, Submitted to Stochastic Analysis and Applications
C. Pfeifer, K. Schredelseker, G. U. H. Seeber, On the negative value of information in informationally inefficient markets. Calculations for large number of traders, Eur. J. Operat. Res., 195 (1) (2009) 117-126.
All possible different paths (sequences of partial sums) in case of n=3:
{0,-1,-2,-3}; median=-1.5
{0,-1,-2,-1}; median=-1
{0,-1,0,-1}; median=-0.5
{0,-1,0,1}; median=0
{0,1,0,-1}; median=0
{0,1,0,1}; median=0.5
{0,1,2,1}; median=1
{0,1,2,3}; median=1.5
sequence of integers in case of n=3: 1,1,1,1
Sequence in context: A142728 A316111 A316348 * A201067 A210320 A165856
Christian Pfeifer (christian.pfeifer(AT), Oct 28 2008, May 04 2010

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