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].
35, 35, 245, 245, 735, 735, 1225, 1225, 1225, 1225, 735, 735, 245, 245, 35, 35
Offset: 0
Examples
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
References
- Pfeifer, C. (2010) Probability distribution of the median taken on partial sums of the simple random walk, Submitted to Stochastic Analysis and Applications
Links
- 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.
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