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Turnpike Property of Stochastic Linear-Quadratic Optimal Control Problems in Large Horizons with Regime Switching I: Homogeneous Cases
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This paper is concerned with optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike properties for the optimal pairs. The key is to prove a proper convergence of the solutions to the differential Riccati equations to the algebraic Riccati equation. Even for the problems without regime switchings, our result provides a refined estimate compared to those in the previous literature, which also provides a new tool for further research.
Forward citations
Cited by 3 Pith papers
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Turnpike properties in linear quadratic Gaussian N-player differential games
Finite-horizon LQ N-player differential games with Gaussian data exhibit exponential turnpike convergence to ergodic equilibria uniformly in N.
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Long-time behavior and turnpike properties of linear-quadratic graphon mean field control problems
Finite-horizon optimal pairs in linear-quadratic graphon mean field control converge exponentially to the ergodic optimal pair away from time boundaries.
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Turnpike properties for zero-sum stochastic linear quadratic differential games of Markovian regime switching system
Finite-horizon optimal feedback gains in zero-sum stochastic linear-quadratic games with regime switching converge exponentially to infinite-horizon gains, yielding a turnpike theorem for the optimal triple.
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