

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



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

0,1


COMMENTS

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 noncooperating 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



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



KEYWORD

fini,full,nonn


AUTHOR

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


EXTENSIONS



STATUS

approved



