Related papers: A new approach to fluctuations of reflected L\'{e}…

For given two standard processes with no positive jumps, we construct, using the excursion theory, a Markov process whose positive and negative motions have the same law as the two processes. The resulting process is a generalization of…

Event-by-event fluctuations of the chemical composition of the hadronic final state of relativistic heavy-ion collisions carry valuable information on the properties of strongly interacting matter produced in the collisions. However, in…

The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events…

We analyze fluctuations of random walks with generally distributed increments. Integral representations for key performance measures are obtained by extending an inversion theorem of Hewitt [11] for Laplace-Stieltjes transforms. Another…

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…

Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However,…

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…

Fluctuation relations are identities, holding in non-equilibrium systems, that have attracted a lot of interest in the last 20 years. This is a series of 4 lectures discussing various aspects of such relations for stochastic equations…

We derive fluctuation-response inequalities for Markov jump processes that link the fluctuations of general observables to the response to perturbations in the transition rates within a unified framework. These inequalities are derived…

In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…

In this article we refine well-known results concerning the fluctuations of one-dimensional random walks. More precisely, if $(S_n)_{n \geq 0}$ is a random walk starting from 0 and $r\geq 0$, we obtain the precise asymptotic behavior as…

The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected L\'evy processes. Like a Brownian motion, which is a weak limit of random walks,…

The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…

We propose a new method for the estimation of a semiparametric tempered stable L\'{e}vy model. The estimation procedure combines iteratively an approximate semiparametric method of moment estimator, Truncated Realized Quadratic Variations…

We investigate a refracted Levy process driven by a jump diffusion process, whose jumps have rational Laplace transforms. For such a stochastic process, formulas for the Laplace transform of its occupation times are deduced. To derive the…

We develop a unified fluctuation-response theory in the frequency domain for nonequilibrium steady states governed by overdamped Langevin dynamics and Markov jump processes. The relation expresses the power spectrum of general observables…

A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many…

Recently Mayer et al. [Phys. Rev. E {\bf 68}, 016116 (2003)] proposed a new way to compute numerically the fluctuation-dissipation ratios in nonequilibrium critical systems. Using well-known facts of nonequilibrium critical dynamics I show…

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…

In this paper, we derive identities for the upward and downward exit problems and resolvents for a process whose motion changes between two L\'evy processes if it is above (or below) a barrier $b$ and coincides with a Poissonian arrival…