Establishes a stochastic viscosity solution framework using semimartingale test functions for BSHJB equations with jumps, proving DPP, existence via measurable selection and Ito-Kunita formula, and uniqueness under super-parabolicity.
Viscosity solutions for HJB equations on the process space: Application to mean field control with common noise
5 Pith papers cite this work. Polarity classification is still indexing.
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UNVERDICTED 5representative citing papers
Establishes existence and uniqueness for optimal policies in continuous-time entropy-regularized mean-field control with common noise via an integrated q-function, plus explicit Gaussian characterization in the LQ setting.
A comparison principle for viscosity solutions of nonlinear PDEs on finite nonnegative measures is proved and used to characterize the value function of a controlled branching McKean-Vlasov diffusion as the unique viscosity solution of the associated HJB equation.
Develops SMP for non-convex mean-field control with joint law dependence and Poisson common noise via relaxed controls and extension transformation, then derives equivalent HJB on measure space.
Establishes existence of optimal controls for constrained mean-field problems with singular controls and derives associated SMP and constrained FBSDEs using relaxed formulation and Lagrange multipliers.
citing papers explorer
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Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations with Jumps
Establishes a stochastic viscosity solution framework using semimartingale test functions for BSHJB equations with jumps, proving DPP, existence via measurable selection and Ito-Kunita formula, and uniqueness under super-parabolicity.
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Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations
Establishes existence and uniqueness for optimal policies in continuous-time entropy-regularized mean-field control with common noise via an integrated q-function, plus explicit Gaussian characterization in the LQ setting.
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Comparison of viscosity solutions for a class of non-linear PDEs on the space of finite nonnegative measures
A comparison principle for viscosity solutions of nonlinear PDEs on finite nonnegative measures is proved and used to characterize the value function of a controlled branching McKean-Vlasov diffusion as the unique viscosity solution of the associated HJB equation.
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Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation
Develops SMP for non-convex mean-field control with joint law dependence and Poisson common noise via relaxed controls and extension transformation, then derives equivalent HJB on measure space.
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Constrained mean-field control with singular controls: Existence, stochastic maximum principle and constrained FBSDE
Establishes existence of optimal controls for constrained mean-field problems with singular controls and derives associated SMP and constrained FBSDEs using relaxed formulation and Lagrange multipliers.