Related papers: Phase velocity and phase diffusion in periodically…
This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general…
This paper proposes an adaptive time-stepping mothods for stochastic diffusion systems whose drift and diffusion coefficients are locally Lipschitz continuous and may exhibit polynomial growth. By controlling the growth of both the drift…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
In this article we investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and non-collective dissipators. Exploiting the permutation symmetry in our model, we…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…
We consider stochastic discrete event dynamic systems that have time evolution represented with two-dimensional state vectors through a vector equation that is linear in terms of an idempotent semiring. The state transitions are governed by…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
In this article we examine the dynamics of a colloidal particle driven by a modulated force over a sinusoidal optical potential energy landscape. Coupling between the competing frequencies of the modulated drive and that of particle motion…
The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one,…
Motivated by networked systems in random environment and controlled hybrid stochastic dynamic systems, this work focuses on modeling and analysis of a class of switching diffusions consisting of continuous and discrete components. Novel…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
We study a non Markovian three state model, subjected to an external periodic signal. This model is intended to describe an excitable systems with periodical driving. In the limit of a small amplitude of the external signal we derive…
The theory for manifestation of stochastic appearance of embryos in the global decay of metastable phase has been constructed. The regime of droplets growth is supposed to be both free molecular one and diffusion one. The deviation for a…