### Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise

Barbu V, Röckner M, Zhang D (2018)
The Annals of Probability 46(4): 1957-1999.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Abstract / Bemerkung
We analyze the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrodinger equation perturbed by a linear multiplicative Wiener process. The existence of an open-loop optimal control and first-order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. Moreover, our approach in particular applies to the deterministic case.
Stichworte
Backward stochastic equation; nonlinear Schrodinger equation; optimal; control; Wiener process
Erscheinungsjahr
2018
Zeitschriftentitel
The Annals of Probability
Band
46
Ausgabe
4
Seite(n)
1957-1999
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2930270

### Zitieren

Barbu V, Röckner M, Zhang D. Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. The Annals of Probability. 2018;46(4):1957-1999.
Barbu, V., Röckner, M., & Zhang, D. (2018). Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. The Annals of Probability, 46(4), 1957-1999. doi:10.1214/17-AOP1217
Barbu, V., Röckner, M., and Zhang, D. (2018). Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. The Annals of Probability 46, 1957-1999.
Barbu, V., Röckner, M., & Zhang, D., 2018. Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. The Annals of Probability, 46(4), p 1957-1999.
V. Barbu, M. Röckner, and D. Zhang, “Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise”, The Annals of Probability, vol. 46, 2018, pp. 1957-1999.
Barbu, V., Röckner, M., Zhang, D.: Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise. The Annals of Probability. 46, 1957-1999 (2018).
Barbu, Viorel, Röckner, Michael, and Zhang, Deng. “Optimal bilinear control of nonlinear stochastic Schrödinger equations driven by linear multiplicative noise”. The Annals of Probability 46.4 (2018): 1957-1999.

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