Vidyashankar,A.N.(1994): Large deviations for branching processes in fixed and random environments, Ph.D. Thesis, Departments of Mathematics and Statistics, Iowa State University, Ames, IA 50011.  Home/Search   Document Not in Database   Summary   Related Articles

.... Gamma l:v 1 Delta v j ffl) 3.13) exists and is positive and finite. 2 As in the single type case further refinements and other large deviation results concerning multitype branching processes have been developed and can be found in Athreya and Vidyashankar ( 25] and [26] and Vidyashankar([60]) We now describe the critical case. This result was obtained by Joffe and Spitizer (see [60] Theorem 13. Let ae = 1 and u and v be as in (3.3) Let oe 2 ij j E(Z 2 1j jZ 0 = i) Gamma m 2 ij 1 for all i; j: Then for any initial Z 0 6= 0, and any w such that w Delta v 0 and 0 x ....

....type case further refinements and other large deviation results concerning multitype branching processes have been developed and can be found in Athreya and Vidyashankar ( 25] and [26] and Vidyashankar( 60] We now describe the critical case. This result was obtained by Joffe and Spitizer (see [60]) Theorem 13. Let ae = 1 and u and v be as in (3.3) Let oe 2 ij j E(Z 2 1j jZ 0 = i) Gamma m 2 ij 1 for all i; j: Then for any initial Z 0 6= 0, and any w such that w Delta v 0 and 0 x 1 lim n 1 P ( w Delta Z n n xjZ n 6= 0) 1 Gamma e Gammax=fl (3.14) where fl ....

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Vidyashankar,A.N.(1994): Large deviations for branching processes in fixed and random environments, Ph.D. Thesis, Departments of Mathematics and Statistics, Iowa State University, Ames, IA 50011.

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