  In this paper, we obtain sharp asymptotic formulas with error estimates for
the Mellin convolution of functions, and use these formulas to characterize the
asymptotic behavior of marginal distribution densities of stock price processes
in mixed stochastic models. Special examples of mixed models are jump-diffusion
models and stochastic volatility models with jumps. We apply our general
results to the Heston model with double exponential jumps, and make a detailed
analysis of the asymptotic behavior of the stock price density, the call option
pricing function, and the implied volatility in this model. We also obtain
similar results for the Heston model with jumps distributed according to the
NIG law.
