Related papers: Is Kyle's equilibrium model stable?
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
We study the scenarios of the dynamics of ternary statistical experiments, modeled employing difference equations. The important features are a balance condition and the existence of a steady-state (equilibrium). We give a classification of…
In this paper we show that when individuals in a bipartite network exclusively choose partners and exchange valued goods with their partners, then there exists a set of exchanges that are pair-wise stable. Pair-wise stability implies that…
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
We investigate a market with a normal-speed informed trader (IT) who may employ mixed strategy and multiple anticipatory high-frequency traders (HFTs) who are under different inventory pressures, in a three-period Kyle's model. The pure-…
This paper considers the stability of tidal equilibria for planetary systems in which stellar rotation provides a significant contribution to the angular momentum budget. We begin by applying classic stability considerations for two bodies…
In this paper we consider a class of generalized Kyle-Back strategic insider trading models in which the insider is able to use the dynamic information obtained by observing the instantaneous movement of an underlying asset that is allowed…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…
We observe that a simple condition suffices to describes non-forking independence over models in a stable theory. Under mild assumptions, this description can be extended to non-forking independence over algebraically closed subsets,…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
The Keen model is a mathematical model that describes the dynamic evolution of wages, employment, and debt based on the known Minsky's Financial Instability Hypothesis. It consists of three first order nonlinear ordinary differential…
A detailed analysis of the stability of equilibriums and bifurcations of the two-dimensional autonomous competitive Lotka-Volterra dynamical system is performed. Necessary and sufficient conditions are determined for equilibriums (without…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
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…
We study the numerical algorithm and error analysis for the Cahn-Hilliard equation with dynamic boundary conditions. A second-order in time, linear and energy stable scheme is proposed, which is an extension of the first-order stabilized…
Instabilities of equilibrium quantum mechanics are common and well-understood. They are manifested for example in phase transitions, where a quantum system becomes so sensitive to perturbations that a symmetry can be spontaneously broken.…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…