
The author raised the question: Start the process at an arbitrary time s and check what happens to its distribution in a fixed time interval [t,\(\infty)\) as the starting time s goes backward to -\(\infty\). Backward limits are considered for time-inhomogeneous regenerative processes introduced by the author [Adv. Appl. Probab. 15, 531-561 (1983; Zbl 0512.60080)]. The existence of a two-sided time-inhomogeneous limit (in the sense of total variation) process, which inherits the regenerative properties, is proved, under regularity conditions on the regeneration times.
Markov processes, inhomogeneous regeneration, inhomogeneous Markov process, General theory of stochastic processes, regeneration times, Generalized stochastic processes, regenerative process, 60G07, existence of a two-sided time-inhomogeneous limit, two-sided process, 60J99, Backward limits, 60G20, regenerative properties
Markov processes, inhomogeneous regeneration, inhomogeneous Markov process, General theory of stochastic processes, regeneration times, Generalized stochastic processes, regenerative process, 60G07, existence of a two-sided time-inhomogeneous limit, two-sided process, 60J99, Backward limits, 60G20, regenerative properties
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