Hamiltonian ODE ’ s in the Wasserstein space of probability measures

  title={Hamiltonian ODE ’ s in the Wasserstein space of probability measures},
  author={Luigi Ambrosio and Wilfrid Gangbo},
In this paper we consider a Hamiltonian H on P2(R), the set of probability measures with finite quadratic moments on the phase space R2d = Rd ×Rd, which is a metric space when endowed with the Wasserstein dis tanceW2. We study the initial value problemdμt/dt+∇ · (Jdvt μt) = 0, whereJd is the canonical symplectic matrix,μ0 is prescribed,vt is a tangent vector toP2(R) at μt , and belongs to∂H(μt), the subdifferential of H at μt . Two methods for constructing solutions of the evolutive system are… CONTINUE READING
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