Related papers: Numerical algorithms for mean exit time and escape…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
This work is concerned with existence of weak solutions to discon- tinuous stochastic differential equations driven by multiplicative Gaus- sian noise and sliding mode control dynamics generated by stochastic differential equations with…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
The escape of particles through a narrow absorbing gate in confined domains is a abundant phenomenon in various systems in physics, chemistry and molecular biophysics. We consider the narrow escape problem in a cellular flow when the two…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
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 consider some special classes of L\'evy processes with no gaussian component whose L\'evy measure is of the type $\pi(dx)=e^{\gamma x}\nu(e^x-1) dx$, where $\nu$ is the density of the stable L\'evy measure and $\gamma$ is a positive…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
We consider the problem of risk-sensitive control of a stochastic network. In controlling such a network, an escape time criterion can be useful if one wishes to regulate the occurrence of large buffers and buffer overflow. In this paper a…
Riccati differential equations is the class of first-order and quadratic ordinary differential equations and has various applications in the systems and control theory. In this paper, we analyze a switched Riccati differential equation that…
We present a general geometrical approach to the problem of escape from a metastable state in the presence of noise. The accompanying analysis leads to a simple condition, based on the norm of the drift field, for determining whether…
Rare events in the first-passage distributions of jump processes are capable of triggering anomalous reactions or series of events. Estimating their probability is particularly important when the jump probabilities have broad-tailed…
A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random $N\times N$ matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and…
We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…