Abstract
A new statistical description of branched chain reactions is suggested. Within its framework the process is characterized in terms of the age and length of linear sequences. The following assumptions are used: (a) there is a single type of active intermediates which is generated with a constant rate: (b) the propagation and termination events may be described by means of a set of formation and consumption rates with time independent apparent rate constants. The joint probability density for the age and length may be computed exactly. We show that this probability density evolves towards a time-persistent form even if the total amount of the reaction intermediate cannot reach a stationary value. If the generation rate is equal to zero or if the total amount of the active intermediate evolves towards an infinite large value then the statistical properties of age and length depend only on the nature of the propagation steps. If the branching factor is near unity then the age and length are strongly correlated.
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