A sensitivity analysis reduces nonlinear Kolmogorov PDEs (nonlinearity from ε-neighborhood max over drifts/diffusions) to a linear PDE plus ε times a second linear PDE, enabling efficient high-dimensional Monte Carlo approximation with error bounds.
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Proves existence results and set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs, with consequences for optimal control and G-Brownian motion.
Proves existence of mean field limits, particle approximations, and set-valued propagation of chaos for controlled McKean-Vlasov SPDEs in a variational framework, illustrated on stochastic porous media equations.
citing papers explorer
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Numerical method for nonlinear Kolmogorov PDEs via sensitivity analysis
A sensitivity analysis reduces nonlinear Kolmogorov PDEs (nonlinearity from ε-neighborhood max over drifts/diffusions) to a linear PDE plus ε times a second linear PDE, enabling efficient high-dimensional Monte Carlo approximation with error bounds.
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Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs
Proves existence results and set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs, with consequences for optimal control and G-Brownian motion.
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A limit theory for controlled McKean-Vlasov SPDEs
Proves existence of mean field limits, particle approximations, and set-valued propagation of chaos for controlled McKean-Vlasov SPDEs in a variational framework, illustrated on stochastic porous media equations.