Related papers: Free L\'evy Processes on Dual Groups
We investigate the existence of affine realizations for term structure models driven by L\'evy processes. It turns out that we obtain more severe restrictions on the volatility than in the classical diffusion case without jumps. As special…
Several long-time limit theorems of one-dimensional L\'{e}vy processes weighted and normalized by functions of the local time are studied. The long-time limits are taken via certain families of random times, called clocks: exponential…
We define a L\'evy process on a smooth manifold $M$ with a connection as a projection of a solution of a Marcus stochastic differential equation on a holonomy bundle of $M$, driven by a holonomy-invariant L\'evy process on a Euclidean…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…
In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect…
We find the group of equivalence transformations for equations of the form $y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a complete group classification of these families of equations, using a direct method…
This paper investigates homomorphisms \`a la Bercovici-Pata between additive and multiplicative convolutions. We also consider their matricial versions which are associated with measures on the space of Hermitian matrices and on the unitary…
In this paper we analyse time change equations (TCEs) for L\'evy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial value problems (IVPs) which are easier to handle. Properties…
We consider a general d-dimensional Levy-type process with killing. Combining the classical Dyson series approach with a novel polynomial expansion of the generator A(t) of the Levy-type process, we derive a family of asymptotic…
A short proof is given of a necessary and sufficient condition for the normalized occupation measure of a L\'evy process in a metrizable compact group to be asymptotically uniform with probability one.
Levy processes, which have stationary independent increments, are ideal for modelling the various types of noise that can arise in communication channels. If a Levy process admits exponential moments, then there exists a parametric family…
By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…
A theory of double affine and special double affine bundles, i.e. differential manifolds with two compatible (special) affine bundle structures, is developed as an affine counterpart of the theory of double vector bundles. The motivation…
We introduce a category of dual pairs of finite locally free algebras over a ring. This gives an efficient way to represent finite locally free commutative group schemes. We give a number of algorithms to compute with dual pairs of…
In this paper we derive exact large-buffer asymptotics for a two-class Generalized Processor Sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed L\'evy processes.…
In this paper, we establish the existence of moments and moment estimates for L\'evy-type processes. We discuss whether the existence of moments is a time dependent distributional property, give sufficient conditions for the existence of…
In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…
We study and relate certain actions and extensions involving 2-groups.
The paper is devoted to a systematic study of the duality of processes in the sense that $E f(X_t^x,y)=E f (x, Y_t^y)$ for a certain $f$. This classical topic has well known applications in interacting particles, intertwining,…