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- W2080485374 abstract "Let {X ij; i>0, j>0} be a double sequence of i.i.d. random variables taking values in the d-dimensional integer lattice E d . Also let $$S_{mn} = sumlimits_{i = 1}^m {sumlimits_{j = 1}^n {X_{ij} } } $$ . Then the range of random walk {S mn: m>0, n>0} up to time (m, n), denoted by R mn , is the cardinality of the set {S pq: 0<p≦m, 0<q≦n}, i.e., the number of distinct points visited by the random walk up to time (m, n). In this paper a sufficient condition in terms of the characteristic function of X 11 is given so that $$lim frac{{R_{mn} }}{{ER_{mn} }} = 1$$ a.s. as either (m, n) or m(n) tends to infinity." @default.
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- W2080485374 date "1978-01-01" @default.
- W2080485374 modified "2023-09-27" @default.
- W2080485374 title "The range of two-parameter random walk in space" @default.
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- W2080485374 doi "https://doi.org/10.1007/bf00537540" @default.
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