THE GROWTH RATE OF RANDOM BALANCING SEQUENCE
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In the present paper, a random sequence is defined by the binary recurrence Zn+1 = AαZn - qZn-1, where α is a random variable which assumes the values +1 and -1 with probability 1=2 each where A is a positive integer and q is a non-zero integer. Furthermore by taking A = 6 and q = 1, the random balancing case has been defined and the remaining cases for A and q have been further tackled. Apart from that an elementary proof regarding the bounds of the expected value for the absolute value of the n-th term in the random balancing sequence has been provided. Moreover, the bounds for the variance of the absolute value of the n-th term has also been obtained. Furthermore, the growth rate of the random sequence has been graphically depicted.
Abstract
In the present paper, a random sequence is defined by the binary recurrence Zn+1 = AαZn - qZn-1, where α is a random variable which assumes the values +1 and -1 with probability 1=2 each where A is a positive integer and q is a non-zero integer. Furthermore by taking A = 6 and q = 1, the random balancing case has been defined and the remaining cases for A and q have been further tackled. Apart from that an elementary proof regarding the bounds of the expected value for the absolute value of the n-th term in the random balancing sequence has been provided. Moreover, the bounds for the variance of the absolute value of the n-th term has also been obtained. Furthermore, the growth rate of the random sequence has been graphically depicted.
참고문헌 (9)
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