Related papers: Stochastic actions for diffusive dynamics: Reweigh…
We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for…
The longstanding question of how stochastic behaviour arises from deterministic Hamiltonian dynamics is of great importance, and any truly holistic theory must be capable of describing this transition. In this review, we introduce the…
This work is devoted to the investigation of the most probable transition path for stochastic dynamical systems driven by either symmetric $\alpha$-stable L\'{e}vy motion ($0<\alpha<1$) or Brownian motion. For stochastic dynamical systems…
A path information is defined in connection with the probability distribution of paths of nonequilibrium hamiltonian systems moving in phase space from an initial cell to different final cells. On the basis of the assumption that these…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
We provide an overview on how to use the measurable selection techniques to derive the dynamic programming principle for a general stochastic optimal control/stopping problem. By considering its martingale problem formulation on the…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
We study the large-time behaviour of Brownian particles moving through a viscous medium in a confined potential, and which are further subjected to position-dependent driving forces that are periodic in time. We focus on the case where…
The coordinated and efficient distribution of limited resources by individual decisions is a fundamental, unsolved problem. When individuals compete for road capacities, time, space, money, goods, etc., they normally make decisions based on…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
The double distribution function approach is an efficient route towards extension of kinetic solvers to compressible flows. With a number of realizations available, an overview and comparative study in the context of high speed compressible…
We analytically investigate the dynamic behavior of an an-isotropic active Brownian particle under various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to…
In this article we show a robustness theorem for controlled stochastic differential equations driven by approximations of Brownian motion. Often, Brownian motion is used as an idealized model of a diffusion where approximations such as…
Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We…
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise…
As written by statistician George Box "All models are wrong, but some are useful", standard diffusion derivation or Feynman path ensembles use nonphysical infinite velocity/kinetic energy nowhere differentiable trajectories - what seems…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position. The derivative is a linear map represented by a multiplicative functional for…
Random walks of particles on a lattice are a classical paradigm for the microscopic mechanism underlying diffusive processes. In deterministic walks, the role of space and time can be reversed, and the microscopic dynamics can produce quite…