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].

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

Offset: 0

Author

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

Keywords

• fini
• full
• nonn

Comments

1) A146207=A146205+(0,A146206), see lemma 2 in 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).

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: 1,2,1
		

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.

Crossrefs

Cf. A137272, A146205, A146207.

Extensions

Keyword:full added by R. J. Mathar, Sep 17 2009