In particular the DMBP is positive recurrent if and only if the MBP is supercritical and the zero state is accessible, in which case the limiting-stationary law of the DMBP is geometric.
If the zero state is inaccessible for the MBP, then it is absorbing and accessible for the DMBP. In this case there is a limiting conditional law (Theorem 3).
The second contribution is an account of limit theorems for the DMBP when S is not positive recurrent.
In Section 3 we supplement the discussion of the definitions of the DMBP in .
As we mentioned in the introduction, three equivalent definitions of the DMBP are presented in .
Definition (iii) is that the DMBP is a Markov process whose transition function has the dual branching property
Gonzalez-Perez M, Milori DMBP, Colnago LA, Martin-Neto L, Melo WJA (2007) Laser-induced fluorescence spectroscopic study of organic matter in a Brazilian oxisol under different tillage systems.
Martin-Neto L, Silva WTL, Milori DMBP (2004) 'Humic substances and soil and water environment.' (Rima Embrapa: Sao Carlos, Brazil)
Martin-Neto L, Milori DMBP, Silva WTL, Simoes ML (2009) EPR, FTIR, Raman.
Milori DMBP, Martin-Neto L, Bayer C, Mielniczuk J, Bagnato VS (2002) Humification degree of soil humic acids determined by fluorescence spectroscopy.
Milori DMBP, Galeti HVA, Martin-Neto L, Dieckow J, Gonzalez-Perez M, Bayer C, Saltan JC (2006) Organic matter study of whole soil samples using laser-induced fluorescence spectroscopy.
Santos LM, Simoes ML, Silva WTL, Milori DMBP, Montes CR, Melfi AJ, Martin-Neto L (2009) Caracterizafao quimica e espectroscopica de solos irrigados com efluente de esgoto tratado.