Related papers: Stochastic systems with memory and jumps
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
The dichotomy between noise-stable and (completely) noise-sensitive stochastic models is of recent interest in probability theory. Of particular interest is the study of lattice models coming from statistical physics. The Fourier transform…
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is…
Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…
Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
Stochastic resetting and noise-enhanced stability are two phenomena which can affect the lifetime and relaxation of nonequilibrium states. They can be considered as measures of controlling the efficiency of the completion process when a…
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
Accurate state estimation requires careful consideration of uncertainty surrounding the process and measurement models; these characteristics are usually not well-known and need an experienced designer to select the covariance matrices. An…
We introduce a new numerical algorithm for solving the stochastic neural field equation (NFE) with delays. Using this algorithm we have obtained some numerical results which illustrate the effect of noise in the dynamical behaviour of…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or…
We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-$m$ distribution. We show that the associated Master equation can be written as a spatial…
Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…
A continuously measured quantum system with multiple jump channels gives rise to a stochastic process described by random jump times and random emitted symbols, representing each jump channel. While much is known about the waiting time…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…