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We study the asymptotic relations between certain singular and constrained control problems for one-dimensional diffusions with both discounted and ergodic objectives. By constrained control problems we mean that controlling is allowed only…
We design receding horizon control strategies for stochastic discrete-time linear systems with additive (possibly) unbounded disturbances, while obeying hard bounds on the control inputs. We pose the problem of selecting an appropriate…
Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…
This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The…
We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it…
We study solutions of a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
We study an optimal control problem on infinite horizon for a controlled stochastic differential equation driven by Brownian motion, with a discounted reward functional. The equation may have memory or delay effects in the coefficients,…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
Transport phenomena in spatially periodic systems far from thermal equilibrium are considered. The main emphasize is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal…
In systems possessing spatial or dynamical symmetry breaking, Brownian motion combined with symmetric external input signals, deterministic or random, alike, can assist directed motion of particles at the submicron scales. In such cases,…
We solve two stochastic control problems in which a player tries to minimize or maximize the exit time from an interval of a Brownian particle, by controlling its drift. The player can change from one drift to another but is subject to a…
We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
We consider an optimal control problem, where a Brownian motion with drift is sequentially observed, and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not…
We study in this paper a class of constrained linear-quadratic (LQ) optimal control problem formulations for the scalar-state stochastic system with multiplicative noise, which has various applications, especially in the financial risk…
In this article, we consider a receding horizon control of discrete-time state-dependent jump linear systems, particular kind of stochastic switching systems, subject to possibly unbounded random disturbances and probabilistic state…
This paper investigates a singular stochastic control problem for a multi-dimensional regime-switching diffusion process confined in an unbounded domain. The objective is to maximize the total expected discounted rewards from exerting the…
We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality…
Motivated by linear-quadratic optimal control problems (LQ problems, for short) for mean-field stochastic differential equations (SDEs, for short) with the coefficients containing regime switching governed by a Markov chain, we consider an…