Related papers: Epigenetics as a first exit problem
The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…
Stability problem of the Wonham filter with respect to initial conditions is addressed. The case of ergodic signals is revisited in view of a gap in the classic work of H. Kunita (1971). We give new bounds for the exponential stability…
We consider generic differential equations in $\mathbb{R}$ with a finite number of hyperbolic equilibria, which are subject to $\omega$--periodic instantaneous perturbative pulses ($\omega>0$). Using the time-$ \omega$ map of the original…
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…
This paper investigates steady state solutions of a vasculogenesis model governed by coupled partial differential equations in a bounded two dimensional domain. Explicit steady state solutions are analytically constructed, and their…
The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent…
In this paper, problems of optimal control are considered where in the objective function, in addition to the control cost there is a tracking term that measures the distance to a desired stationary state. The tracking term is given by some…
Input-to-State Stability (ISS) is fundamental in mathematically quantifying how stability degrades in the presence of bounded disturbances. If a system is ISS, its trajectories will remain bounded, and will converge to a neighborhood of an…
The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the…
In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $\alpha$-stable L\'evy type noise from a 2-dimensional disk. For an appropriate choice of parameters the mean first passage…
The authors consider stochastic aspects of the stabilization problem for two and three-dimensional Oseen equations with help of feedback control defined on a part of the fluid boundary. Stochastic issues arise when inevitable unpredictable…
Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative…
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by infinite peaks on a coherently constructed potential energy landscape. It is then important to ask what such…
The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A…
In this paper, we show that the quasi-one-dimensional flow of an ideal inviscid fluid in a corrugated pipe is parametrically unstable in certain frequency bands. First-order perturbation theory is used to analyze the stability of the flow,…
A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and…
In this manuscript we consider the stability of periodic solutions to Lambda-Omega lattice dynamical systems. In particular, we show that an appropriate ansatz casts the lattice dynamical system as an infinite-dimensional fast-slow…
This paper deals with existence and robust stability of hybrid limit cycles for a class of hybrid systems given by the combination of continuous dynamics on a flow set and discrete dynamics on a jump set. For this purpose, the notion of…
Toward explaining the persistence of biased inferences, we propose a framework to evaluate competing (mis)specifications in strategic settings. Agents with heterogeneous (mis)specifications coexist and draw Bayesian inferences about their…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…