Related papers: Fluctuation theory for one-sided L\'evy processes …
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
We obtain a new fluctuation identity for a general L\'{e}vy process giving a quintuple law describing the time of first passage, the time of the last maximum before first passage, the overshoot, the undershoot and the undershoot of the last…
A refracted L\'evy process is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable size) whenever the aggregate process is above a pre-specified level. More precisely, whenever it exists, a refracted…
Thermally activated phenomena in physics and chemistry, such as conformational changes in biomolecules, liquid film rupture, or ferromagnetic field reversal, are often associated with exponentially long transition times described by…
Using the fluctuation theorem supplemented with geometric arguments, we derive universal features of the (long-time) efficiency fluctuations for thermal and isothermal machines operating under steady or periodic driving, close or far from…
In this paper, we solve exit problems for a level-dependent L\'evy process which is exponentially killed with a killing intensity that depends on the present state of the process. Moreover, we analyse the respective resolvents. All…
We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat''…
We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as…
We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…
We provide a novel expression of the scale function for a L\'evy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for…
The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some…
Products of random $2\times 2$ matrices exhibit Gaussian fluctuations around almost surely convergent Lyapunov exponents. In this paper, the distribution of the random matrices is supported by a small neighborhood of order $\lambda>0$ of…
We present results of the numerical simulations and the scaling characteristics of one-dimensional random fluctuations with heavy tailed probability distribution functions. Assuming that the distribution function of the random fluctuations…
The last couple of years has seen a remarkable number of new, explicit examples of the Wiener-Hopf factorization for Levy processes where previously there had been very few. We mention in particular the many cases of spectrally negative…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
For one-dimensional symmetric L\'{e}vy processes, which hit every point with positive probability, we give sharp bounds for the tail function of the first hitting time of B which is either a single point or an interval. The estimates are…
We derive the extended fluctuation theorems in presence of multiple measurements and feedback, when the system is governed by Hamiltonian dynamics. We use only the forward phase space trajectories in the derivation. However, to obtain an…
For refracted spectrally negative L\'evy processes, we identify expressions of several quantities related to Laplace transforms on their weighted occupation times until first exit times. Such quantities are expressed in terms of unique…
We estimate a median of $f(X_t)$ where $f$ is a Lipschitz function, $X$ is a L\'evy process and $t$ an arbitrary time. This leads to concentration inequalities for $f(X_t)$. In turn, corresponding fluctuation estimates are obtained under…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…