Let {Xt1,t2:t1,t2 ³ 0}{X_{t_{1},t_{2}}:t_{1},t_{2}geq0} be a two-parameter Lévy process on ℝ d . We study basic properties of the one-parameter process {X x(t),y(t):t∈T} where x and y are, respectively, nondecreasing and nonincreasing nonnegative continuous functions on the interval T. We focus on and characterize the case where the process has stationary increments.
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