Geodesic
Pathological Birth-and-Death Processes and the Spectral Theory of Strings
Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 74-78

Voir la notice de l'article provenant de la source Math-Net.Ru

In a 1957 paper, Karlin and McGregor discovered the existence of birth-and-death processes for which the Chapman–Kolmogorov equation does not hold. Such processes are said to be pathological. We disclose the probability nature of pathological birth-and-death processes with the help of M. Krein's spectral theory of strings.
Keywords: birth-and-death process, string, spectral theory, generalized diffusion process. 
@article{FAA_2005_39_2_a7,
     author = {I. S. Kats},
     title = {Pathological {Birth-and-Death} {Processes} and the {Spectral} {Theory} of {Strings}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {74--78},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a7/}
}
TY  - JOUR
AU  - I. S. Kats
TI  - Pathological Birth-and-Death Processes and the Spectral Theory of Strings
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2005
SP  - 74
EP  - 78
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a7/
LA  - ru
ID  - FAA_2005_39_2_a7
ER  - 
%0 Journal Article
%A I. S. Kats
%T Pathological Birth-and-Death Processes and the Spectral Theory of Strings
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2005
%P 74-78
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a7/
%G ru
%F FAA_2005_39_2_a7
I. S. Kats. Pathological Birth-and-Death Processes and the Spectral Theory of Strings. Funkcionalʹnyj analiz i ego priloženiâ, Tome 39 (2005) no. 2, pp. 74-78. http://geodesic.mathdoc.fr/item/FAA_2005_39_2_a7/