Related papers: Finite Variation of Fractional Levy Processes
This article focuses on properties of monotone convolutions. A criterion for infinite divisibility and time evolution of convolution semigroups are mainly studied. In particular, we clarify that many analogues of the classical results of…
In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain a closed analytic expressions for the form factors, the Debye functions and their asymptotic…
We consider the problem of estimating the fractional order of a L\'{e}vy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
We consider a probabilistic approach to compute the Wiener--Young $\Phi$-variation of fractal functions in the Takagi class. Here, the $\Phi$-variation is understood as a generalization of the quadratic variation or, more generally, the…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
We consider the regularity of sample paths of Volterra-L\'{e}vy processes. These processes are defined as stochastic integrals $$ M(t)=\int_{0}^{t}F(t,r)dX(r), \ \ t \in \mathds{R}_{+}, $$ where $X$ is a L\'{e}vy process and $F$ is a…
The study of non-stationary processes whose local form has controlled properties is a fruitful and important area of research, both in theory and applications. We present here a construction of multifractional multistable processes, based…
We consider solutions of L\'evy-driven stochastic differential equations of the form $\mathrm{d} X_t=\sigma(X_{t-})\mathrm{d} L_t$, $X_0=x$ where the function $\sigma$ is twice continuously differentiable and maximal of linear growth and…
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…
We construct a modified continuous-state branching process whose Malthusian parameter is replaced by another when passing below a certain level. The construction is obtained via a Lamperti-like transform applied to a refracted L\'evy…
In this paper, we consider certain $\sigma$-finite measures which can be interpreted as the output of a linear filter. We assume that these measures have regularly varying tails and study whether the input to the linear filter must have…
There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
We show on- and off-diagonal upper estimates for the transition densities of symmetric Levy and Levy-type processes. To get the an-diagonal estimates we prove a Nash type inequality for the related Dirichlet form. For the off-diagonal…
In this work, we investigate the fine regularity of L\'evy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities…
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…
A version of the saddle point method is developed, which allows one to describe exactly the asymptotic behavior of distribution densities of Levy driven stochastic integrals with deterministic kernels. Exact asymptotic behavior is…
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 address L\'{e}vy-stable stochastic processes in bounded domains, with a focus on a discrimination between inequivalent proposals for what a boundary data-respecting fractional Laplacian (and thence the induced random process) should…