相关论文: A Counterexample to the L\'evy Flight Foraging Hyp…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…

With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging…

In this paper, we introduce branching processes in a L\'evy random environment. In order to define this class of processes, we study a particular class of non-negative stochastic differential equations driven by Brownian motions and Poisson…

Soaring birds gain energy from stable ascending currents or shear. However, it remains unclear whether energy loss due to drag can be overcome by extracting work from transient turbulent fluctuations. We designed numerical simulations of…

We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of L\'evy walks, in which transport is driven by a convex combination of fractional material derivatives and a source…

Efficient search acts as a strong selective force in biological systems ranging from cellular populations to predator-prey systems. The search processes commonly involve finding a stationary or mobile target within a heterogeneously…

We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0,K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value…

There lies a latent danger in utilizing some known mathematical results in ecology. Some results do not apply to the problem at hand. We identify one such trend. Based on a couple of theorems in mathematical statistics, Link (2013) cautions…

We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions…

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…

We propose a model for the structure formation of jellyfish swimming based on active Brownian particles. We address the phenomena of counter-current swimming, avoidance of turbulent flow regions and foraging. We motivate corresponding…

Control of non-episodic, finite-horizon dynamical systems with uncertain dynamics poses a tough and elementary case of the exploration-exploitation trade-off. Bayesian reinforcement learning, reasoning about the effect of actions and future…

This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…

A cascaded online learning flight control system has been developed and enhanced with respect to action smoothness. In this paper, we investigate the convergence performance of the control system, characterized by the increment of a…

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of…

Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…

We map the problem of diffusion in the quenched trap model onto a new stochastic process: Brownian motion which is terminated at the coverage "time" ${\cal S}_\alpha=\sum_{x=-\infty} ^\infty (n_x)^\alpha$ with $n_x$ being the number of…

Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…

We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by…