Viscosity solutions of nonlinear integro-differential equations

Olivier Alvarez; Agnès Tourin

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 3, page 293-317
  • ISSN: 0294-1449

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Alvarez, Olivier, and Tourin, Agnès. "Viscosity solutions of nonlinear integro-differential equations." Annales de l'I.H.P. Analyse non linéaire 13.3 (1996): 293-317. <http://eudml.org/doc/78384>.

@article{Alvarez1996,
author = {Alvarez, Olivier, Tourin, Agnès},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {backward nonlinear integro-differential equation; sub- and supersolutions; Perron's method; mathematical finance; stochastic utility model; viscosity solutions},
language = {eng},
number = {3},
pages = {293-317},
publisher = {Gauthier-Villars},
title = {Viscosity solutions of nonlinear integro-differential equations},
url = {http://eudml.org/doc/78384},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Alvarez, Olivier
AU - Tourin, Agnès
TI - Viscosity solutions of nonlinear integro-differential equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 3
SP - 293
EP - 317
LA - eng
KW - backward nonlinear integro-differential equation; sub- and supersolutions; Perron's method; mathematical finance; stochastic utility model; viscosity solutions
UR - http://eudml.org/doc/78384
ER -

References

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  1. [1] G. Barles and B. Perthame, Comparison principle for Dirichlet-type Hamilton-Jacobi equations and singular perturbation of degenerated elliptic equations, Appl. Math. Optim., Vol. 21, 1990, pp. 21-44. Zbl0691.49028MR1014943
  2. [2] A. Bensoussan and J.L. Lions, Contrôle Impulsionnel et Inéquations Quasi Variationnelles., Dunod, Paris, 1982. Zbl0491.93002MR673169
  3. [3] M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc., Vol. 27, 1992, pp. 1-67. Zbl0755.35015MR1118699
  4. [4] D. Duffie and L. Epstein, Stochastic differential utility, Econometrica, Vol. 60, 1992, pp. 353-394. Zbl0763.90005MR1162620
  5. [5] D. Duffie and P.L. Lions, PDE solutions of stochastic differential utility, J. Math. Econ., Vol. 21, 1992, pp. 577-606. Zbl0768.90006MR1195678
  6. [6] I.I. Gihman and A.V. Skorohod, The Theory of Stochastic Processes, Vol. 3, Springer, Berlin, 1979. Zbl0404.60061
  7. [7] H. Ishii, Perron's method for Hamilton-Jacobi equations, Duke Math. J., Vol. 55, 1987, pp. 369-384. Zbl0697.35030MR894587
  8. [8] C. Ma, Intertemporal recursive utility in the presence of mixed Poisson-Brownian uncertainty, 1993, Mc Gill University, Montreal, Canada. Working paper series 14. 
  9. [9] E. Pardoux and S.G. Peng, Adapted solutions of a backward stochastic differential equation, Systems Control Let., Vol. 14, 1990, pp. 55-61. Zbl0692.93064MR1037747
  10. [10] A. Sayah, Equations d'Hamilton-Jacobi du premier ordre avec termes intégro-différentiels, Parties I & II. Comm P.D.E., Vol. 16, 1991, pp. 1057-1093. Zbl0742.45004
  11. [11] H.M. Soner, Optimal control with state-space constraint II, SIAM J. Control Optim., Vol. 24, 1986, pp. 1110-1122. Zbl0619.49013MR861089
  12. [12] H.M. Soner, Optimal control of jump-Markov processes and viscosity solutions, in Stochastic Differential Systems, Stochastic Control Theory and Applications, (W. H. Fleming and P. L. Lions, eds.), IMA Math. Appl., Vol. 10, Springer, Berlin, 1988, pp. 501-511. Zbl0850.93889MR934740

Citations in EuDML Documents

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  1. Mariko Arisawa, A new definition of viscosity solutions for a class of second-order degenerate elliptic integro-differential equations
  2. Guy Barles, Cyril Imbert, Second-order elliptic integro-differential equations : viscosity solutions' theory revisited
  3. Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
  4. Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
  5. Dan Goreac, Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks
  6. Krzysztof A. Topolski, On the vanishing viscosity method for first order differential-functional IBVP

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