Random walks in random environments of a general type. (English) Zbl 0828.60054
Summary: A notion of (multidimensional) random walk in random environment of functional type is introduced in a semimartingale form. Some estimates (useful for limit theorems) are presented. The inverse problem – the estimation of the parameters of environments given the trajectories of random walks – is discussed. A limit theorem for the case of functionally-depending random environment is proved.
MSC:
| 60G50 | Sums of independent random variables; random walks |
| 60G44 | Martingales with continuous parameter |
References:
| [1] | Liptser, R. Sh. and Shiryaev, A. N. 1989. ”Theory of Martingales”. Dordrecht: Kluwer Academic Publishers. · doi:10.1007/978-94-009-2438-3 |
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| [4] | Kabanov Yu. M., Mathem. Sbornik 107 pp 364– (1978) |
| [5] | Oblakova T. V., Moscow State University pp 1– (1990) |
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