Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control

By Marco Fuhrman, Gianmario Tessitore. 2002

184 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/76a406a4352f5a654fc4aff1cb67345f75cf47ee

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Citations in the corpus

Optimal control of path-dependent McKean–Vlasov SDEs in infinite-dimension (2020, unknown): “[20, 48, 49, 64, 44]) stochastic reaction-diffusion equations (see e.”
Ergodic BSDEs under weak dissipative assumptions (2010, background): “In connection with stochastic equations, the space G1 has been introduced in [9], to which we refer the reader for further properties.”
Infinite horizon backward stochastic differential equations and elliptic equations in Hilbert spaces (2004, methodology): “In the general case, but with finite horizon, the result is contained in [12] and in [26].”
Optimal control of a stochastic heat equation with boundary-noise and boundary-control (2007, methodology): “14) we have Z(s, t, x) = [∇v(λ − A)1−β ](s, X(s, t, x)) (λ−A)βb and the role of G in [14], Theorem 7.”
Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations (2005, background): “5 in [18], Xn belongs to L1,2(H) and there exists a version of DXn such that for every s ∈ [0, T ), {DsX τ , τ ∈ (s, T ]} is a predictable process in L2(Ξ,H) with continuous paths satisfying, P-a.”
Stochastic optimal control of delay equations arising in advertising models (2004, methodology): “In this case the L2 approach of Goldys and Gozzi [13] and the forward-backward SDE approach of Fuhrman and Tessitore [10], [12], [11] apply.”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “We refer to Fuhrman and Tessitore (2002) for the related references.”
Wong-Zakai approximations of stochastic evolution equations (2006, methodology): “Following [8] and [42] we introduce a class of maps acting among Banach spaces, possessing regularity properties weaker than Fréchet differentiability.”
BSDEs with stochastic Lipschitz condition and quadratic PDEs in Hilbert spaces (2007, methodology): “This problem of regular dependence of the solution of a stochastic forward–backward system has been studied for finite dimensions by Pardoux and Peng [21], by El Karoui, Peng and Quenez [9], by Tang [24], and, for infinite dimensions, by Fuhrman and Tessitore in [10,11].”