Related papers: Potential Theory of Normal Tempered Stable Process

This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…

We present a feedback protocol that is able to confine a system to a single micro-state without heat dissipation. The protocol adjusts the Hamiltonian of the system in such a way that the Bayesian posterior distribution after measurement is…

This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…

We present a stochastic description of a model of N mutually repelling active spheres in the presence of external fields and characterize its steady state behavior. To reproduce the effects of the experimentally observed persistence of the…

This paper provides a multivariate extension of Bertoin's pathwise construction of a L\'evy process conditioned to stay positive/negative. Thus obtained processes conditioned to stay in half-spaces are closely related to the original…

Fluctuation Theorems are statements about the entropy of systems far from thermal equilibrium. In this Letter relativistic Fluctuation Theorems for Brownian motion are presented and proven. Though there is a known discretization dilemma…

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we…

We give an explicit representation for the transition law of a tempered stable Ornstein-Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation of increments from this process. Our results apply to…

We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for…

We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a…

We investigate a random integral which provides a natural example of an imaginary exponential functional of Brownian motion. This functional shows up in the study of the binary annihilation process, within the Doi-Peliti formalism for…

We consider a coupled bistable N-particle system driven by a Brownian noise, with a strong coupling corresponding to the synchronised regime. Our aim is to obtain sharp estimates on the metastable transition times between the two stable…

Estimates of densities of convolution semigroups of probability measures are given under specific assumptions on the corresponding L\'evy measure and the L\'evy--Khinchin exponent. The assumptions are satisfied, e.g., by tempered stable…

We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…

We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosi\'nsky (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and…

We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle etc.), that is confined by an external potential. Focusing on the limit in…

The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences…

We study a class of stochastic differential equations driven by a possibly tempered L{\'e}vy process, under mild conditions on the coefficients. We prove the well-posedness of the associated martingale problem as well as the existence of…

Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends…

Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical…