Hull Options Futures Solution Manual 4the Edition

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Binary chaos

1. One-dimensional case

infinite binary sequences
chaotic , if and only if, for any positive integer N
all options for its final subsequence of length N
have a uniform distribution, ie each such option
meets otn.chastotoy 2 ^-N .

finite binary sequence of length 2 ^N ,
closed in a ring, N- kvazihaotichna , if and only if,
all options for its final subsequence of length N
have a uniform distribution, ie each such option
meets otn.chastotoy 2 ^-N .

Obviously, the N- kvazihaotichnaya sequence
with K \u0026lt;N is also a K- kvazihaotichnoy .

N = 1: 01 01 ...
N = 2: 0011 0011 ...
N = 3: 00010111 00010111 ...
N = 4: 0000100110101111 0000100110101111 ...


2. Two-dimensional case

infinite binary plane chaotic ,
if and only if, for any positive integers M and N
all variants of the rectangle length and width of M
N have a uniform distribution,
ie each such option meets otn.chastotoy 2 ^{- (M + N)} .