The Annals of Applied Probability

Perturbation analysis and Malliavin calculus

L. Decreusefond
Source: Ann. Appl. Probab. Volume 8, Number 2 (1998), 496-523.

Abstract

Using the Malliavin calculus, we give a unified treatment of the so-called perturbation analysis of dynamic systems. Several applications are also given.

First Page: Show Hide
Primary Subjects: 60H07, 60H30
Secondary Subjects: 60G55
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1028903536
Digital Object Identifier: doi:10.1214/aoap/1028903536
Mathematical Reviews number (MathSciNet): MR1624953
Zentralblatt MATH identifier: 0952.60050

References

BACCELLI, F., KLEIN, M. and ZUy EV, S. 1995. Perturbation analysis of functionals of random measures. Adv. in Appl. Probab. 27 306 325. Z.
Mathematical Reviews (MathSciNet): MR96d:60070
Zentralblatt MATH: 0829.60041
Digital Object Identifier: doi:10.2307/1427827
BASS, R. F. and CRANSTON, M. 1986. The Malliavin calculus for pure jump processes and applications to local time. Ann. Probab. 14 490 532. Z.
Mathematical Reviews (MathSciNet): MR88b:60113
Zentralblatt MATH: 0595.60044
Digital Object Identifier: doi:10.1214/aop/1176992528
Project Euclid: euclid.aop/1176992528
BIANE, P. 1989. Chaotic representation for finite Markov chains. Stochastics Stochastics Rep. 30 61 68. Z.
Mathematical Reviews (MathSciNet): MR1085480
Zentralblatt MATH: 0712.60049
BICHTELER, K. and JACOD, J. 1983. Calcul de Malliavin pour les diffusions avec sauts: existence d'une densite dans le cas unidimensionnel. Seminaire de Probabilites XVII 132 157. ´ ´ ´ Springer, New York. Z.
Mathematical Reviews (MathSciNet): MR86f:60070
BISMUT, J.-M. 1983. Calcul des variations stochastiques et processus de sauts. Zeitschrift fur ¨ Wahrscheinlichkeits Theory 63 147 235. Z.
Mathematical Reviews (MathSciNet): MR85a:60077
Zentralblatt MATH: 0494.60082
Digital Object Identifier: doi:10.1007/BF00538963
BLASZCZy SZy N, B. 1995. Factorial moment expansion for stochastic sy stems. Stochastic Process. Z. Appl. 56 2 321 336. Z.
Mathematical Reviews (MathSciNet): MR96e:60085
Digital Object Identifier: doi:10.1016/0304-4149(94)00071-Z
BREMAUD, P. 1992. Maximal coupling and rare perturbation sensitivity analysis. Queuing ´ Z. Sy stems Theory Appl. 11 4 307 333. Z.
Mathematical Reviews (MathSciNet): MR93j:93039
Digital Object Identifier: doi:10.1007/BF01163859
BREMAUD, P. and VAZQUEZ-ABAD, F. J. 1992. On the pathwise computation of derivatives with ´ ´ respect to the rate of a point process: the phantom RPA method. Queuing Sy stems Z. Theory Appl. 10 3 249 269. Z.
Mathematical Reviews (MathSciNet): MR93d:60154
Digital Object Identifier: doi:10.1007/BF01159209
DECREUSEFOND, L. 1994. Methode de perturbation pour les reseaux de files d'attente. Ph.D. ´ ´ ´ dissertation, Ecole Nationale Superieure des Telecommunications. ´ ´ ´ Z.
DEVETSIKIOTIS, M., WAEL, A. A.-Q., FREEBERSy SER, J. A. and TOWNSEND, J. K. 1993. Stochastic gradient techniques for the efficient simulation of high-speed networks using importance sampling. IEEE Trans. Comm. XX 751 756. Z.
GLASSERMAN, P. 1990. Gradient Estimation via Perturbation Analy sis. Kluwer, Dordrecht. Z.
GLy NN, P. W. 1987. Likelihood ratio gradient simulation: an overview. In Proceedings of the Z. 1987 Winter Simulation Conference A. Thesen, H. Grant and W. Kelton, eds.. Z.
HEIDELBERGER, P. 1987. Limitations of infinitesimal perturbation analysis. Technical Report, Bell Labs, Yorktown Heights, NY. Z.
HO, Y. C. and CAO, X. R. 1983. Perturbation analysis and optimization of queueing networks. J. Optim. Theory Appl. 40 559 582. Z.
Zentralblatt MATH: 0496.90034
Mathematical Reviews (MathSciNet): MR717177
Digital Object Identifier: doi:10.1007/BF00933971
HO, Y. C., CAO, X. R. and CASSANDRAS, C. 1983. Infinitesimal and finite perturbation analysis for queueing networks. Automatica 19 439 445. Z.
Zentralblatt MATH: 0514.90028
JACOD, J. 1979. Calcul Stochastique et Problemes de Martingales. Springer, Berlin. Z. L'ECUy ER, P. 1990. A unified view of the IPA, SF and LR gradient estimation techniques. Management Science 36 1364 1383. Z.
Mathematical Reviews (MathSciNet): MR542115
MALLIAVIN, P. 1978. Stochastic calculus of variations and hy poelliptic operators. In Proceedings Z. of the International Sy mposium on S.D.E. K. Ito, ed..
Mathematical Reviews (MathSciNet): MR81f:60083
Zentralblatt MATH: 0411.60060
MOLLER, J. and ZUy EV, S. A. 1996. Gamma-ty pe results and other related properties of Poisson processes. Adv. in Appl. Probab. 28 662 673. Z.
Mathematical Reviews (MathSciNet): MR97g:60021
Digital Object Identifier: doi:10.2307/1428175
NORRIS, J. R. 1987. Integration for jump processes. Seminaire de Probabilites XXII 271 315. ´ ´ Springer, Berlin.Z.
NUALART, D. and VIVES, J. 1988. Anticipative calculus for the Poisson process based on the Fock space. Seminaire de Probabilites XXIV 154 165. Springer, Berlin. ´ ´ Z.
PRIVAULT, N. 1994. Chaotic and variational calculus in discrete and continuous time for the Poisson process. Stochastics Stochastics Rep. 51 83 109. Z.
Mathematical Reviews (MathSciNet): MR97f:60107
Zentralblatt MATH: 0851.60052
REIMAN, M. I. and WEISS, A. 1989a. Light traffic derivatives via likelihood ratios. IEEE Trans. Z. Inform. Theory 35 3. Z.
Mathematical Reviews (MathSciNet): MR1022084
Digital Object Identifier: doi:10.1109/18.30987
REIMAN, M. I. and WEISS, A. 1989b. Sensitivity analysis via likelihood ratios. Oper. Res. 37 830 844.Z.
Mathematical Reviews (MathSciNet): MR1021423
Zentralblatt MATH: 0679.62087
Digital Object Identifier: doi:10.1287/opre.37.5.830
RUIZ DE CHAVEZ, J. 1983. Sur les integrales stochastiques multiples. Seminaire de Probabilites ´ ´ ´ XIX 248 261. Springer, Berlin. Z.
SURI, R. 1989. Perturbation analysis: The state of the art and research issues explained via the GI G 1 queue. Proc. IEEE 77 114 137. Z.
SURI, R. and ZAZANIS, M. 1988. Perturbation analysis gives strongly consistent sensitivity estimates for the M G 1 queues. Management Science 34 39 64. ¨ Z.
Mathematical Reviews (MathSciNet): MR88k:90078
Digital Object Identifier: doi:10.1287/mnsc.34.1.39
USTUNEL, A. S. 1995. An Introduction to Analy sis on Wiener Space. Lecture Notes in Math. ¨ 1610. Springer, Berlin. Z.
ZUy EV, S. A. 1993. Russo's formula for Poisson point fields and its applications. Discrete Math. Appl. 3 63 73.
Mathematical Reviews (MathSciNet): MR1220977

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The Annals of Applied Probability

The Annals of Applied Probability