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We prove asymptotic behaviour of transition density for a large class ofspectrally one-sided L\'evy processes of unbounded variation satisfying mildcondition imposed on the second derivative of the Laplace exponent, orequivalently, on the real part of the characteristic exponent. We also providesharp two-sided estimates on the density when restricted additionally toprocesses without Gaussian component.

Transition densities of spectrally positive L\'evy processes