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Search: id:A146206
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| A146206 |
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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]. |
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+0
4
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| 35, 91, 357, 721, 1575, 2535, 3985, 5210, 3985, 2535, 1575, 721, 357, 91, 35
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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1) A146207=A146205+(0,A146206), see lemma 2 in Pfeifer (2008).
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. 2008).
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REFERENCES
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Pfeifer, C. (2008) Probability distribution of the median taken on partial sums of the simple random walk. Submitted to Stochastic Processes and their Applications.
Pfeifer, C. Schredelseker, K. and Seeber G.U.H. (2008) On the negative value of information in informationally inefficient markets. Calculations for large number of traders. European Journal of Operational Research, in press.
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EXAMPLE
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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
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CROSSREFS
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A137272, A146205, A146207
Sequence in context: A118631 A020295 A020164 this_sequence A044222 A044603 A063795
Adjacent sequences: A146203 A146204 A146205 this_sequence A146207 A146208 A146209
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KEYWORD
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fini,full,nonn
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AUTHOR
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Christian Pfeifer (christian.pfeifer(AT)uibk.ac.at), Oct 28 2008
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EXTENSIONS
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Keyword:full added by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 17 2009
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