Related papers: Positive Harris recurrence for degenerate diffusio…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
In this paper we consider a diffusion process obtained as a small random perturbation of a dynamical system attracted to a stable equilibrium point. The drift and the diffusive perturbation are assumed to evolve slowly in time. We describe…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Dynamic discrete choice models are widely employed to answer substantive and policy questions in settings where individuals' current choices have future implications. However, estimation of these models is often computationally intensive…
In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…
We consider properties of one-dimensional diffusive dichotomous flow and discuss effects of resonant activation in the presence of statistically independent random resetting mechanism. Resonant activation and stochastic resetting are two…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…
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 a discrete-time version of a Hawkes process defined as a Poisson auto-regressive process whose parameters depend on the past of the trajectory. We allow these parameters to take on negative values, modelling inhibition. More…
Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…
Hyperchaos is distinguished from chaos by the presence of at least two positive Lyapunov exponents instead of just one in dynamical systems. A general scenario is presented here that shows emergence of hyperchaos with a sudden large…
In this paper, we consider a diffusion process pertaining to a chain of distributed control systems with small random perturbation. The distributed control system is formed by n subsystems that satisfy an appropriate Hormander condition,…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
We consider a model describing a neuron and the input it receives from its dendritic tree when this input is a random perturbation of a periodic deterministic signal, driven by an Ornstein-Uhlenbeck process. The neuron itself is modeled by…