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We study monotone and convex stochastic orders for processes with independentincrements. Our contributions are twofold: First, we relate stochastic ordersof the Poisson component to orders of their (generalized) L\'evy measures. Therelation is proven using an interpolation formula for infinitely divisiblelaws. Second, we derive explicit conditions on the characteristics of theprocesses. In this case, we prove the conditions via constructions ofcouplings.

Monotone and Convex Stochastic Orders for Processes with Independent Increments