J. Villarroel, M. Montero
Given a renewal process (N_t) with events at epochs (t_n)_(n=1,2...) we consider the "Age'' or backward recurrence time t->A_t:=t-t_{N_t}. We investigate the conditional distribution of this Markov process. We also study interesting functionals like the maximum at time t: (M_t= sup_(s<t) A_s) and give a Laplace transform of the distribution. By comparison with the maximum after n cycles we show that asymptotically it is described by a Gumbel distribution. Other interesting observables like recurrence properties are considered. Records of this process are partially related to previous issues.
Palabras clave / Keywords: renewal process, backward recurrence time
Programado
Sesión V11 Procesos Estocásticos
1 de junio de 2018 17:20
Sala 4
