A local limit theorem on one-sided large deviations for dominated-variation distributions

R. A. Doney, A large deviation local limit theorem,Math. Proc. Camb. Phil. Soc.,105, 575–577 (1989). C. Klüppelberg, Subexponential distributions and integrated tails,J. Appl. Probab.,25, 132–142 (1988). S. M. Berman, The tail of the convolution of densities and its application to a model of HIV-latency time,Ann. Appl. Probab.,2, 481–502 (1992). P. Embrechts and E. Omey, A property of long-tailed distributions,J. Appl. Probab.,21, 80–87 (1984). V. V. Petrov,Sums of Independent Random Variables. Springer, Berlin-New York (1975). N. H. Bingham, C. M. Goldie, and J. L. Teugels,Regular Variation. Cambridge University Press (1987). S. V. Nagaev, On asymptotic behavior of probabilities of one-side large deviations,Teor. Veroyatn. Primen.,26, 362–372 (1981). A. Baltrūnas, On asymptotics of probabilities of one-sided large deviations.Lith. Math. J.,35, 11–17 (1995).