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

0,1

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).

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

Table of n, a(n) for n=0..14.

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.

Example

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

Crossrefs

Cf. A137272, A146205, A146207.

Sequence in context: A300554 A020295 A020164 * A350196 A259978 A044222

Adjacent sequences: A146203 A146204 A146205 * A146207 A146208 A146209

Keyword

fini,full,nonn

Author

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

Extensions

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

Status

approved