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An intrinsic calculus of variations for functionals of laws of semi-martingales

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  • Lassalle, Rémi
  • Cruzeiro, Ana Bela

Abstract

We develop a calculus of variations for functionals on a space of laws of continuous stochastic processes, which extends the classical one. We extend Hamilton’s least action principle and Noether’s theorem to this generalized framework. As an application we obtain, under mild conditions, a stochastic Euler−Lagrange condition and invariants for the critical points of recent problems in stochastic control, namely for semi-martingale optimal transportation problems.

Suggested Citation

  • Lassalle, Rémi & Cruzeiro, Ana Bela, 2019. "An intrinsic calculus of variations for functionals of laws of semi-martingales," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3585-3618.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:3585-3618
    DOI: 10.1016/j.spa.2018.10.001
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    References listed on IDEAS

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    1. Mikami, Toshio & Thieullen, Michèle, 2006. "Duality theorem for the stochastic optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1815-1835, December.
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