On the number of coincidences of two homogeneous random walks with positive increments
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I. A. Kravchenko
Abstract
We investigate the distribution of the random variable equal to the number of coincidences of two homogeneous random walks with positive independent increments. This random variable is the length of the subsequence of common elements in two random sequences which are random subsequences of the same random sequence. For the considered random variable we obtain the asymptotic expression for the mathematical expectation and a limit theorem under the assumption that the sequential intervals between coincidences of the two random walks have a finite variance. For the particular case of random walks with increments equal to 1 and 2 we prove a finiteness of this variance and obtain the expression of the variance in terms of the parameters of the random walks.
© de Gruyter 2010
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- Calculation of limit probabilities of the distribution of permanent of a random matrix over the field GF(p)
- On the number of coincidences of two homogeneous random walks with positive increments
- Plane sections of the generalised Pascal pyramid and their interpretations
- On proper colourings of hypergraphs using prescribed colours
- On large distances between neighbouring zeros of the Riemann zeta-function
- On some algebraic and combinatorial properties of correlation-immune Boolean functions
- Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements
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Articles in the same Issue
- Calculation of limit probabilities of the distribution of permanent of a random matrix over the field GF(p)
- On the number of coincidences of two homogeneous random walks with positive increments
- Plane sections of the generalised Pascal pyramid and their interpretations
- On proper colourings of hypergraphs using prescribed colours
- On large distances between neighbouring zeros of the Riemann zeta-function
- On some algebraic and combinatorial properties of correlation-immune Boolean functions
- Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements
- A complete solution of the minimisation problem for a set of binary two-tape automata
