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In this paper one presents the extension of the transient analysis of theclass of continuous-time birth and death processes defined on non-negativeintegers with special transitions from and to the origin. From the origintransitions can occur to any state. But being in any other state, besidesordinary transitions to neighbouring states, a transition to the origin canoccur. All possible transition intensities are assumed to be non-randomfunctions of time and may depend on the state of the process. We improvepreviously known ergodicity and truncation bounds for this class of processeswhich were known only for the case when transitions from the origin decayexponentially (other intensities must have unique uniform upper bound). We showhow the bounds can be obtained the decay rate is slower than exponential.Numerical results are also provided.

Ergodicity and uniform in time truncation bounds for inhomogeneous birth and death processes with additional transitions from and to origin