Abstract
We define ℕo={0,1,...}and say that a stochastic process X ={X(n); n ∈ ℕ0 N} is an N-parameter, ℤd-valued, additive random walk, if there are N independent random walks X1, ... , X N on Zd, such that
Here, nj denotes the jth coordinate of n ∈ ℕ0 N and we are following the standard convention of starting our (ordinary) random walks at the origin. That is, Xj (0) = 0 for all j = 1, … ,N. From now on, N will always denote the temporal dimension and d the spatial one, in accordance with the conventional language of stochastic processes.
This research was partially supported by an NSF grant and a grant from NATO.
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Khoshnevisan, D., Xiao, Y. (2000). Images and Level Sets of Additive Random Walks. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_21
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DOI: https://doi.org/10.1007/978-1-4612-1358-1_21
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