Geodesic
Dynamics of random chains of finite size with an infinite number of elements in $ {\mathbb R}^{2} $
Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 58-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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A finite chain with infinitely many units within the stochastic dynamical model in $ {\mathbb R}^{2}$ is considered. The equation for the probability distribution density of chain lengths is constructed. This equation is a function of the parameter $t$ which stands for the time. This research is a sequel to work [1].
Keywords: Random chain, expectation function, limit behavior, characteristic function, convergence in quadratic mean, SDE. 
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Elena V. Karachanskaya (Chalykh). Dynamics of random chains of finite size with an infinite number of elements in $ {\mathbb R}^{2} $. Teoriâ slučajnyh processov, Tome 16 (2010) no. 2, pp. 58-68. http://geodesic.mathdoc.fr/item/THSP_2010_16_2_a6/

[1] V. A. Doodko, E. V. Chalykh, The dynamics of finite chain which has infinite many of units in $ \mathbb{R}^{2}$, Preprint. The Inst. for Appl. Math., The FEB of Rus. Ac. Sci., Dal'nauka, Vladivostok, 1998 (in Russian)

[2] W. Feller, An Introduction to Probability Theory and its Applications, v. 1, Wiley, New York, 1968

[3] A. D. Wentzel, A Course in the Theory of Stochastic Processes, McGraw-Hill, New York, 1981