Related papers: Stochastic Models for the 3x+1 and 5x+1 Problems

From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying…

We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by…

Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

Many exo-solar systems discovered in the last decade consist of planets orbiting in resonant configurations and consequently, their evolution should show long-term stability. However, due to the mutual planetary interactions a multi-planet…

We derive the equations of celestial mechanics governing the variations of the orbital elements under a stochastic perturbation generalizing the classical Gauss equations. Explicit formulas are given for the semi-major axis, the…

Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump…

The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…

We present a survey on the results on a particular coagulation-fragmentation model given by the Becker-D\"oring equations. For both the deterministic and stochastic versions, we include well-posedness, long-time behavior, convergence rate…

Past research on pedestrian trajectory forecasting mainly focused on deterministic predictions which provide only point estimates of future states. These future estimates can help an autonomous vehicle plan its trajectory and avoid…

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…

This paper contrasts recursive state space models and direct multi-step predictors for linear predictive control. We provide a tutorial exposition for both model structures to solve the following problems: 1. stochastic optimal control; 2.…

This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…

This paper presents two variations of a novel stochastic prediction algorithm that enables mobile robots to accurately and robustly predict the future state of complex dynamic scenes. The proposed algorithm uses a variational autoencoder to…

Since their introduction, anchoring methods in extragradient-type saddlepoint problems have inspired a flurry of research due to their ability to provide order-optimal rates of accelerated convergence in very general problem settings. Such…

We investigate perturbations in the Kepler problem. We offer an overview of the dynamical system using Newtonian, Lagrangian and Hamiltonian Mechanics to build a foundation for analyzing perturbations. We consider the effects of a…

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our…

The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…