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arXiv · 2610.01545

Vector- and operator-valued backward stochastic equations with finite-variation drivers and a maximum principle for singular stochastic control in infinite dimensions

Ying Hu·Guomin Liu·Shanjian Tang
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Abstract

We study a mixed regular--singular control problem for stochastic evolution equations in a Hilbert space with possibly unbounded random linear operators, a nonconvex regular-control domain, and a state-dependent singular coefficient. The singular control is an adapted nondecreasing càdlàg process whose terminal value need not be bounded. We prove well-posedness and weighted moment estimates for the forward and backward equations, and characterize the second-order adjoint by a conditionally expected operator-valued backward stochastic integral equation. An Itô-type formula for the quadratic form of this adjoint, together with spike and convex variations, yields a second-order Hamiltonian condition for the regular control, as well as nonnegativity and a contact condition for the optional singular Hamiltonian.

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Ying Hu, Guomin Liu, Shanjian Tang. 2026-10-01. Vector- and operator-valued backward stochastic equations with finite-variation drivers and a maximum principle for singular stochastic control in infinite dimensions. https://arxiv.org/abs/2610.01545

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