  In queueing theory, Lorden's inequality can be used for bounds estimation of
the moments of backward and forward renewal times. Two random variables called
backwards renewal time and forward renewal time for this process are defined.
Lorden's inequality it's true for the renewal process, so expectations of
backward and forward renewal times are bounded by the relation of expectation
of moment of the random variable for any fixed moment of time, where random
variables are i.i.d. We generalised and proved a similar result for dependent
random variables with finite expectations, some constant C and integrable
function Q(s): if X is not independent and have absolutely continuous
distribution function which satisfies some boundary conditions, then the
analogue of Lorden's inequality for renewal process is true. In August 2021
reviewed version is uploaded.
