Law of large numbers for a class of superdiffusions
Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 2, pp. 171-185.
@article{AIHPB_2006__42_2_171_0,
     author = {Engl\"ander, J\'anos and Winter, Anita},
     title = {Law of large numbers for a class of superdiffusions},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {171--185},
     publisher = {Elsevier},
     volume = {42},
     number = {2},
     year = {2006},
     doi = {10.1016/j.anihpb.2005.03.004},
     zbl = {1093.60058},
     mrnumber = {2199796},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.03.004/}
}
TY  - JOUR
AU  - Engländer, János
AU  - Winter, Anita
TI  - Law of large numbers for a class of superdiffusions
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2006
DA  - 2006///
SP  - 171
EP  - 185
VL  - 42
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2005.03.004/
UR  - https://zbmath.org/?q=an%3A1093.60058
UR  - https://www.ams.org/mathscinet-getitem?mr=2199796
UR  - https://doi.org/10.1016/j.anihpb.2005.03.004
DO  - 10.1016/j.anihpb.2005.03.004
LA  - en
ID  - AIHPB_2006__42_2_171_0
ER  - 
%0 Journal Article
%A Engländer, János
%A Winter, Anita
%T Law of large numbers for a class of superdiffusions
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2006
%P 171-185
%V 42
%N 2
%I Elsevier
%U https://doi.org/10.1016/j.anihpb.2005.03.004
%R 10.1016/j.anihpb.2005.03.004
%G en
%F AIHPB_2006__42_2_171_0
Engländer, János; Winter, Anita. Law of large numbers for a class of superdiffusions. Annales de l'I.H.P. Probabilités et statistiques, Volume 42 (2006) no. 2, pp. 171-185. doi : 10.1016/j.anihpb.2005.03.004. http://www.numdam.org/articles/10.1016/j.anihpb.2005.03.004/

[1] I. Chavel, L. Karp, Large time behavior of the heat kernel: the parabolic λ-potential alternative, Comment. Math. Helv. 66 (1991) 541-556. | Zbl

[2] D.A. Dawson, Measure-valued Markov processes, in: Hennequin P.L. (Ed.), École d'été de probabilités de Saint Flour XXI, 1991, Lecture Notes in Math., vol. 1541, Springer-Verlag, Berlin, 1993, pp. 1-260. | MR | Zbl

[3] P. Donnelly, T.G. Kurtz, Particle representations for measure-valued population models, Ann. Probab. 27 (1) (1999) 166-205. | MR | Zbl

[4] E.B. Dynkin, Branching particle systems and superprocesses, Ann. Probab. 19 (3) (1991) 1157-1194. | MR | Zbl

[5] E.B. Dynkin, Diffusions, Superdiffusions and Partial Differential Equations, Amer. Math. Soc. Colloq. Publ., vol. 50, Amer. Math. Soc., Providence, RI, 2002. | MR | Zbl

[6] J. Engländer, An example and a conjecture concerning scaling limits of superdiffusions, Statist. Probab. Lett. 66 (3) (2004) 363-368. | MR | Zbl

[7] J. Engländer, R.G. Pinsky, On the construction and support properties of measure-valued diffusions on DR d with spatially dependent branching, Ann. Probab. 27 (2) (1999) 684-730. | Zbl

[8] J. Engländer, R.G. Pinsky, Uniqueness/nonuniqueness for positive solutions to semilinear equations of the form u t =Lu+Vu-γu P in R n , J. Differential Equations 192 (2) (2003) 396-428. | Zbl

[9] J. Engländer, D. Turaev, A scaling limit theorem for a class of superdiffusions, Ann. Probab. 30 (2) (2002) 683-722. | MR | Zbl

[10] A. Etheridge, An Introduction to Superprocesses, University Lecture Series, vol. 20, Amer. Math. Soc., Providence, RI, 2000. | MR | Zbl

[11] K. Fleischmann, J. Swart, Extinction versus exponential growth in a supercritical super-Wright-Fisher diffusion, Stochastic Process. Appl. 106 (1) (2003) 141-165. | MR | Zbl

[12] J.G. Kemeny, J.L. Snell, A.W. Knapp, Denumerable Markov Chains, Springer-Verlag, 1976. | MR | Zbl

[13] L. Overbeck, Some aspects of the Martin boundary of measure-valued diffusions, in: Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems, Amer. Math. Soc., Providence, RI, 1994, pp. 179-186. | MR | Zbl

[14] Y. Pinchover, Large time behavior of the heat kernel, J. Functional Anal. 206 (1) (2004) 191-209. | MR | Zbl

[15] R.G. Pinsky, Positive Harmonic Functions and Diffusion, Cambridge University Press, 1995. | MR | Zbl

[16] R.G. Pinsky, Transience, recurrence and local extinction properties of the support for supercritical finite measure-valued diffusions, Ann. Probab. 24 (1) (1996) 237-267. | MR | Zbl

[17] B. Simon, Large time behavior of the heat kernel: on a theorem of Chavel and Karp, Proc. Amer. Math. Soc. 118 (2) (1993) 513-514. | MR | Zbl

[18] S. Watanabe, Limit theorems for a class of branching processes, in: Chover J. (Ed.), Markov Processes and Potential Theory, Wiley, New York, 1967, pp. 205-232. | Zbl

Cited by Sources: