Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion

Jean-François Delmas; Pascal Vogt

Annales de l'I.H.P. Probabilités et statistiques (2005)

  • Volume: 41, Issue: 5, page 817-849
  • ISSN: 0246-0203

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Delmas, Jean-François, and 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 41.5 (2005): 817-849. <http://eudml.org/doc/77869>.

@article{Delmas2005,
author = {Delmas, Jean-François, Vogt, Pascal},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {nonlinear boundary value problem; collision local time; exit measure},
language = {eng},
number = {5},
pages = {817-849},
publisher = {Elsevier},
title = {Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion},
url = {http://eudml.org/doc/77869},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Delmas, Jean-François
AU - Vogt, Pascal
TI - Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 5
SP - 817
EP - 849
LA - eng
KW - nonlinear boundary value problem; collision local time; exit measure
UR - http://eudml.org/doc/77869
ER -

References

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  9. [9] P. Hsu, Reflecting Brownian motion, boundary local time and Neumann problem, PhD thesis, Stanford University, 1984. 
  10. [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. Zbl0956.60096MR1765014
  11. [11] J.-F. Le Gall, Spatial Branching Processes, Random Snakes and Partial Differential Equations, Lectures Math., ETH Zürich, Birkhäuser, 1999. Zbl0938.60003MR1714707
  12. [12] B. Maisonneuve, Exit systems, Ann. Probab.3 (1975) 399-411. Zbl0311.60047MR400417
  13. [13] P. Mörters, P. Vogt, A construction of catalytic super-Brownian motion via collision local time, Stochastic Process. Appl.115 (1) (2005) 77-90. Zbl1072.60070MR2105370
  14. [14] S.C. Port, C.J. Stone, Brownian Motion and Classical Potential Theory, Academic Press, 1978. Zbl0413.60067MR492329
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  16. [16] K. Sato, T. Ueno, Multi-dimensional diffusion and the Markov process on the boundary, J. Math. Kyoto Univ.3 (4) (1965) 529-605. Zbl0219.60057MR198547

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