Related papers: Optimal linear responses for Markov chains and sto…
Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
We consider the problem of stabilization of a linear system, under state and control constraints, and subject to bounded disturbances and unknown parameters in the state matrix. First, using a simple least square solution and available…
We provide a link between response theory, pullback measures, and optimal fingerprinting method that paves the way for a) predicting the impact of acting forcings on time-dependent systems and b) attributing observed anomalies to acting…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the…
We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
The maximization of reach-avoid probabilities for stochastic systems is a central topic in the control literature. Yet, the available methods are either restricted to low-dimensional systems or suffer from conservative approximations. To…
Leveraging recent work on data-driven methods for constructing a finite state space Markov process from dynamical systems, we address two problems for obtaining further reduced statistical representations. The first problem is to extract…
Optimal liquidation of an asset with unknown constant drift and stochastic regime-switching volatility is studied. The uncertainty about the drift is represented by an arbitrary probability distribution; the stochastic volatility is…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that…
The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two…
We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degenerate noise. For the associated transfer…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…