Solutions of stochastic partial differential equations as extremals of convex functionals

Acta Mathematica Hungarica

Volumn 109, Issue 1-2, 2005, Pages 127-145

  Gyongy I ^a,b   Martinez T ^a,c  

^a King's Buildings ^*

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Monotone operators; Stochastic partial differential equations

Indexed keywords

EID: 27844454414     PISSN: 02365294     EISSN: 15882632     Source Type: Journal    
DOI: 10.1007/s10474-005-0237-4     Document Type: Article

References (11)

1. I. Gyöngy, On stochastic equations with respect to semimartingales III, Stochastics, 7 (1982), 231-254.
2. I. Gyöngy and N. V. Krylov, On stochastic equations with respect to semimartingales II. Itô formula in Banach spaces, Stochastics, 6 (1982), 153-173.
3. I. Gyöngy and A. Millet, On discretization schemes for stochastic evolution equations, submitted.
4. N. V. Krylov, Extremal properties of solutions of stochastic equations, Theory Probab. Appl., 29 (1984), 209-221.
5. N. V. Krylov and B. L. Rosovskii, Stochastic evolution equations, J. Soviet Mathematics, 16 (1981), 1233-1277.
6. E. Pardoux, Equations aux derivées partielles stochastiques nonlinearies monotones. Etude de solutions fortes de type Ito, Thése Doct. Sci. Math. Univ. Paris Sud. (1975).
7. D. Revuz and M. Yor, Continuous martingales and Brownian Motion, A series of comprehensive studies in Mathematics, 293, Springer (Berlin, 1994).
8. B. L. Rozovskii, Stochastic evolution systems. Linear theory and applications to nonlinear filtering, Kluwer (Dordrecht).
9. K. Yosida, Functional Analysis, Springer-Verlag (Berlin, 1974).
10. E. Zeidler, Nonlinear functional Analysis and its Applications. II/A,B. Nonlinear Monotone Operators, Springer-Verlag (New York, 1990).
11. E. Zeidler, Nonlinear Functional Analysis and its Applications. III. Variational Methods and Optimization, Springer-Verlag (New York, 1990).