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

2016/07/22 by Viorel Barbu, Michael Röckner, Barbu, Viorel +3 · 3 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #35J10 #35Q40 #49K20 #60H15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1607.06652

openalex publication_date 2016/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Here is investigated the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrödinger 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.

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