Related papers: Fluctuation theory for spectrally positive additiv…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
We theoretically study the propagation of light in one-dimensional space- and time-dependent disorder. The disorder is described by a fluctuating permittivity $\epsilon(x,t)$ exhibiting short-range correlations in space and time, without…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
Another way to evaluate the spectral-correlation properties of thermal fields of solids is suggested. Such a method takes into account detailed structure of the interface transition layer separating one bulk region from those of the vacuum…
In this paper, we study fluctuation identities for spectrally negative L\'evy processes killed by a general class of additive functionals. We consider positive co-natural additive functionals (PcNAFs), which include as special cases both…
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any L\'evy process on $[0,T]$ as $T\to\infty$.…
For spectrally negative L\'evy processes, we prove several fluctuation results involving a general draw-down time, which is a downward exit time from a dynamic level that depends on the running maximum of the process. In particular, we find…
Recent fluctuation identities for $\alpha$-stable L\'evy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory…
This paper uses two new ingredients, namely stochastic differential equations satisfied by continuous-state branching processes (CSBPs), and a topology under which the Lamperti transformation is continuous, in order to provide…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
Scale functions play a central role in the fluctuation theory of spectrally negative L\'evy processes. For spectrally negative compound Poisson processes with positive drift, a new representation of the $q$-scale functions in terms of the…
In the paper we consider Lamperti type theorems for random fields. Together with known results we present some new results on ${\mathbb R}^m$-valued self-similar fields $\{{\bf X} ({\bf t}), \ {\bf t} \in {\mathbb R}^d \}$, their domains of…
L\'evy flights for light have been demonstrated in disordered systems with and without optical gain, and remained unobserved in ordered ones. In the present letter, we investigate, numerically and experimentally, L\'evy flights for light in…
Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric field generated by the charge distribution. In Part I of this…
We complement and extend our work on fluctuation relations arising in nonequilibrium systems in steady states driven by L\'evy noise [Phys. Rev. E 76, 020101(R) (2006)]. As a concrete example, we consider a particle subjected to a drag…
We present a class of L\'evy processes for modelling financial market fluctuations: Bilateral Gamma processes. Our starting point is to explore the properties of bilateral Gamma distributions, and then we turn to their associated L\'evy…
This paper provides a framework for investigations in fluctuation theory for L\'evy processes with matrix-exponential jumps. We present a matrix form of the components of the infinitely divisible factorization. Using this representation we…
In this article we derive formula for probability $\Prob(\sup_{t\leq T} (X(t)-ct)>u)$ where $X=\{X(t)\}$ is a spectrally positive L\'evy process and $c\in\RL$. As an example we investigate the inverse Gaussian L\'evy process.
In this paper we present some limit theorems for power variation of L\'evy semi-stationary processes in the setting of infill asymptotics. L\'evy semi-stationary processes, which are a one-dimensional analogue of ambit fields, are moving…
For a positive self-similar Markov process, X, we construct a local time for the random set, $\Theta$, of times where the process reaches its past supremum. Using this local time we describe an exit system for the excursions of X out of its…