Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion
Delmas, Jean-François ; Vogt, Pascal
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005), p. 817-849 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2005__41_5_817_0,
     author = {Delmas, Jean-Fran\c cois and Vogt, Pascal},
     title = {Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {41},
     year = {2005},
     pages = {817-849},
     doi = {10.1016/j.anihpb.2004.05.007},
     mrnumber = {2165252},
     zbl = {1077.60038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2005__41_5_817_0}
}

Delmas, Jean-François; Vogt, Pascal. Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) pp. 817-849. doi : 10.1016/j.anihpb.2004.05.007. http://gdmltest.u-ga.fr/item/AIHPB_2005__41_5_817_0/

[1] R. Abraham, Reflecting Brownian snake and a Neumann-Dirichlet problem, Stochastic Process. Appl. 89 (2000) 239-260. | MR 1780289 | Zbl 1045.60077

[2] R. Abraham, J.-F. Delmas, Solutions of Δu=4u 2 with Neumann’s condition using the Brownian snake, Probab. Theory Related Fields 128 (4) (2004) 475-516. | Zbl 1054.60081

[3] R.F. Bass, Probabilistic Techniques in Analysis, Springer, New York, 1995. | MR 1329542 | Zbl 0817.60001

[4] R. Blumenthal, R. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR 264757 | Zbl 0169.49204

[5] M. Chaleyat-Maurel, N. El Karoui, Un problème de réflexion et ses applications au temps local et aux équations différentielles stochastiques sur R, cas continu, in: Astérisque, vol. 52-53, 1978, pp. 117-144.

[6] J.-F. Delmas, Super-mouvement brownien avec catalyse, Stochastics Stochastics Rep. 58 (3-4) (1996) 303-347. | MR 1424697 | Zbl 0867.60056

[7] T. Duquesne, J.-F. Le Gall, Random trees, Lévy processes and spatial branching processes, Astérisque 281 (2002). | MR 1954248 | Zbl 1037.60074

[8] E. Dynkin, Diffusions, Superdiffusions and Partial Differential Equations, Amer. Math. Soc. Colloq. Publ., vol. 50, American Mathematical Society, 2002. | MR 1883198 | Zbl 0999.60003

[9] P. Hsu, Reflecting Brownian motion, boundary local time and Neumann problem, PhD thesis, Stanford University, 1984.

[10] A. Klenke, A review on spatial catalytic branching, in: Gorostiza L., Ivanoff G. (Eds.), Stochastic Models, A Conference in Honor of Don Dawson, Conference Proceedings, vol. 26, Canadian Mathematical Society, Providence, 2000, pp. 245-264. | MR 1765014 | Zbl 0956.60096

[11] J.-F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures Math., ETH Zürich, Birkhäuser, 1999. | MR 1714707 | Zbl 0938.60003

[12] B. Maisonneuve, Exit systems, Ann. Probab. 3 (1975) 399-411. | MR 400417 | Zbl 0311.60047

[13] P. Mörters, P. Vogt, A construction of catalytic super-Brownian motion via collision local time, Stochastic Process. Appl. 115 (1) (2005) 77-90. | MR 2105370 | Zbl 1072.60070

[14] S.C. Port, C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, 1978. | MR 492329 | Zbl 0413.60067

[15] K. Sato, H. Tanaka, Local times on the boundary for multi-dimensional reflecting diffusion, Proc. Japan Acad. 38 (1962) 699-702. | MR 148109 | Zbl 0138.11302

[16] K. Sato, T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ. 3 (4) (1965) 529-605. | MR 198547 | Zbl 0219.60057