Related papers: Fluctuation theory for one-sided L\'evy processes …
We find an expression for the joint Laplace transform of the law of $(T_{[x,+\infty[},X_{T_{[x,+\infty[}})$ for a L\'evy process $X$, where $T_{[x,+\infty[}$ is the first hitting time of $[x,+\infty[$ by $X$. When $X$ is an $\alpha$-stable…
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of…
In this paper we solve the exit problems for an one-sided Markov additive process (MAP) which is exponentially killed with a bivariate killing intensity $\omega(\cdot,\cdot)$ dependent on the present level of the process and the present…
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take…
This survey aims to review two decades of progress on exponential functionals of (possibly killed) real-valued L\'evy processes. Since the publication of the seminal survey by Bertoin and Yor, substantial advances have been made in…
In the paper the rescaled occupation time fluctuation process of a certain empirical system is investigated. The system consists of particles evolving independently according to \alpha-stable motion in R^d, \alpha<d<2\alpha. The particles…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
We experimentally demonstrate that highly structured distributions of work emerge during even the simple task of erasing a single bit. These are signatures of a refined suite of time-reversal symmetries in distinct functional classes of…
A level-dependent L\'evy process solves the stochastic differential equation $dU(t) = dX(t)-{\phi}(U(t)) dt$, where $X$ is a spectrally negative L\'evy process. A special case is a multi-refracted L\'evy process with…
For a (killed) spectrally negative L\'evy process we provide an analytic expression for the distribution of its overshoot over a fixed level in terms of the infinitesimal generator and the scale function of the process. Our identity…
The fluctuations of the current for the one-dimensional totally asymmetric exclusion process with $L$ sites are studied in the relaxation regime of times $T\sim L^{3/2}$. Using Bethe ansatz for the periodic system with an evolution…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
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…
An investigation of the distribution of finite time trajectory divergence is performed on an Atmospheric Global Circulation Model. The distribution of the largest local Lyapunov exponent shows a significant probability for negative values…
Consider a L\'evy process $Y(t)$ over an exponentially distributed time $T_\beta$ with mean $1/\beta$. We study the joint distribution of the running maximum $\bar{Y}(T_\beta)$ and the time epoch $G(T_\beta$) at which this maximum last…
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for…
In this article, we study the fluctuations of linear eigenvalue statistics of reverse circulant $(RC_n)$ matrices with independent entries which satisfy some moment conditions. We show that $\frac{1}{\sqrt{n}} \text{Tr} \phi(RC_n)$ obey the…
We prove two martingale identities which involve exit times of Levy-driven Ornstein--Uhlenbeck processes. Using these identities we find an explicit formula for the Laplace transform of the exit time under the assumption that positive jumps…
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…