Differentiability of the Feynman-Kac semigroup and a control application
Giuseppe Da Prato; Jerzy Zabczyk
- Volume: 8, Issue: 3, page 183-188
- ISSN: 1120-6330
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topDa Prato, Giuseppe, and Zabczyk, Jerzy. "Differentiability of the Feynman-Kac semigroup and a control application." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.3 (1997): 183-188. <http://eudml.org/doc/244107>.
@article{DaPrato1997,
abstract = {The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.},
author = {Da Prato, Giuseppe, Zabczyk, Jerzy},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Stochastic control problem; Feynman-Kac formula; Hamilton-Jacobi equations; Hamilton-Jacobi-Bellman equation; linear parabolic equation; regular solution},
language = {eng},
month = {10},
number = {3},
pages = {183-188},
publisher = {Accademia Nazionale dei Lincei},
title = {Differentiability of the Feynman-Kac semigroup and a control application},
url = {http://eudml.org/doc/244107},
volume = {8},
year = {1997},
}
TY - JOUR
AU - Da Prato, Giuseppe
AU - Zabczyk, Jerzy
TI - Differentiability of the Feynman-Kac semigroup and a control application
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/10//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 3
SP - 183
EP - 188
AB - The Hamilton-Jacobi-Bellman equation corresponding to a large class of distributed control problems is reduced to a linear parabolic equation having a regular solution. A formula for the first derivative is obtained.
LA - eng
KW - Stochastic control problem; Feynman-Kac formula; Hamilton-Jacobi equations; Hamilton-Jacobi-Bellman equation; linear parabolic equation; regular solution
UR - http://eudml.org/doc/244107
ER -
References
top- CANNARSA, P. - DA PRATO, G., Some results on nonlinear optimal control problems and Hamilton-Jacobi equations infinite dimensions. J. Funct. Anal., 90, 1990, 27-47. Zbl0717.49022MR1047576DOI10.1016/0022-1236(90)90079-Z
- CANNARSA, P. - DA PRATO, G., Direct solution of a second order Hamilton-Jacobi equation in Hilbert spaces. In: G. DA PRATO - L. TUBARO (eds.), Stochastic partial differential equations and applications. PitmanResearch Notes in Mathematics Series n. 268, 1992, 72-85. Zbl0805.49016MR1222689
- DA PRATO, G. - DEBUSSCHE, A., Control of the stochastic Burgers model of turbulence. Scuola Normale Superiore preprint n. 4, Pisa1996. Zbl1111.49302MR1691934DOI10.1137/S0363012996311307
- DA PRATO, G. - ZABCZYK, J., Ergodicity for infinite dimensions. Enciclopedia of Mathematics and its Applications, Cambridge University Press, 1996. Zbl0761.60052MR1417491DOI10.1017/CBO9780511662829
- ELWORTHY, K. D., Stochastic flows on Riemannian manifolds. In: M. A. PINSKY - V. VIHSTUTZ (eds.), Diffusion Processes and Related Problems in Analysis. Birkhäuser, 1992, vol. II, 33-72. Zbl0758.58035MR1187985
- GOZZI, F., Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem. Commun, in partial differential equations, 20 (5&6), 1995, 775-826. Zbl0842.49021MR1326907DOI10.1080/03605309508821115
- GOZZI, F., Global regular solutions of second order Hamilton-Jacobi equations in Hilbert spaces with locally Lipschitz nonlinearities. Journal of Mathematical Analysis and Applications, 198, 1996, 399-443. Zbl0858.35129MR1376272DOI10.1006/jmaa.1996.0090
- GOZZI, F. - ROUY, E., Regular solutions of second order stationary Hamilton-Jacobi equations. J. Differential Equations, to appear. Zbl0864.34058MR1409030DOI10.1006/jdeq.1996.0139
- LIONS, P. L., Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution. Acta Math., 161, 1988, 243-278. Zbl0757.93082MR971797DOI10.1007/BF02392299
- LIONS, P. L., Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control fo Zakai's equation. In: G. DA PRATO - L. TUBARO (eds.), Stochastic Partial Differential Equations and Applications. Lecture Notes in Mathematics No. 1390, Springer-Verlag, 1989, 147-170. Zbl0757.93083MR1019600DOI10.1007/BFb0083943
- LIONS, P. L., Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part III: Uniqueness of viscosity solutions for general second order equations. J. Funct. Anal., 86, 1989, 1-18. Zbl0757.93084MR1013931DOI10.1016/0022-1236(89)90062-1
- PESZAT, S. - ZABCZYK, J., Strong Feller property and irreducibility for diffusions on Hilbert spaces. Annals of Probability, 1996. Zbl0831.60083MR1330765
- SWIECH, A., Viscosity solutions of fully nonlinear partial differential equations with «unbounded» terms in infinite dimensions. Ph. D. Thesis, University of California at Santa Barbara, 1993. MR2690118
Citations in EuDML Documents
top- Giuseppe Da Prato, Arnaud Debussche, Dynamic programming for the stochastic Navier-Stokes equations
- Giuseppe Da Prato, Asymptotic behaviour of stochastic quasi dissipative systems
- Giuseppe Da Prato, Asymptotic behaviour of stochastic quasi dissipative systems
- Giuseppe da Prato, Arnaud Debussche, Dynamic Programming for the stochastic Navier-Stokes equations
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