Geodesic
On the number of coincidences of two homogeneous random walks with positive increments
Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 63-74.

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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. 
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I. A. Kravchenko. On the number of coincidences of two homogeneous random walks with positive increments. Diskretnaya Matematika, Tome 22 (2010) no. 3, pp. 63-74. http://geodesic.mathdoc.fr/item/DM_2010_22_3_a5/

[1] Chvatal V., Sankov D., “Longest common subsequences of two random sequences”, J. Appl. Probab., 12 (1975), 306–315 | DOI | MR | Zbl

[2] Mikhailov V. G., Mezhennaya N. M., “Otsenki dlya veroyatnostei plotnogo vlozheniya odnoi diskretnoi posledovatelnosti v druguyu”, Diskretnaya matematika, 17:3 (2005), 19–27 | MR | Zbl

[3] Mezhennaya N. M., “Predelnye teoremy dlya chisla plotnykh serii v sluchainoi posledovatelnosti”, Diskretnaya matematika, 21:1 (2009), 105–116 | MR

[4] Golic J. D., “Constrained embedding probability for two binary strings”, SIAM J. Discrete Math., 9 (1996), 360–364 | DOI | MR | Zbl

[5] Kravchenko I. A., “O posledovatelnosti obschikh tochek odnorodnykh sluchainykh bluzhdanii s polozhitelnymi prirascheniyami i ikh ispolzovanie dlya otsenki parametrov odnogo sposoba skrytoi peredachi informatsii”, Obozrenie prikladnoi i promyshlennoi matematiki, 14 (2007), 598–609 | Zbl

[6] Petrov V. V., Summy nezavisimykh sluchainykh velichin, Nauka, Moskva, 1972 | MR

[7] Sachkov V. N., Vvedenie v kombinatornye metody diskretnoi matematiki, Nauka, Moskva, 1982 | MR | Zbl