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These assumptions allow for a construction of an unimodal l ́evy process in d+2 with the same characteristic exponent as the original process We develop a general construction for nonlinear l ́evy processes with given characteristics. The relationship between the two processes provides a fruitful source of gradient estimates of transition densities.

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We compared sister species of beetles, one of which, ophraella slobodkini, feeds on the lineage's ancestral host, ambrosia artemisiifolia, while o

Notulata has shifted to a novel host, iva frutescens. For all 0 s t the random variables x (t ) x (s) same distribution