Abstract
Let πα be a Poisson process on ℝd of intensity λ and letW 1(t),W 2 (t),..., be a sequence of independent Wiener processes. LetW i (t)=X i +W i (t) whereX 1,X 2,..., are the points of πα. Consider the processess(t)=#{i:‖X i (t)‖⩽1}. These and related processes are studied.
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Révész, P. Path properties of an infinite system of Wiener processes. J Theor Probab 6, 353–383 (1993). https://doi.org/10.1007/BF01047579
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DOI: https://doi.org/10.1007/BF01047579