Related papers: Levy processes in cones of fuzzy vectors
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised version of Mecke's formula. En passant, it also allows to…
In this paper we consider how to use the convolution method to construct approximations, which consist of fuzzy numbers sequences with good properties, for a general fuzzy number. It shows that this convolution method can generate…
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…
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 introduce and study a new class of partial differential equations (PDEs) with hybrid fuzzy-stochastic parameters, coined fuzzy-stochastic PDEs. Compared to purely stochastic PDEs or purely fuzzy PDEs, fuzzy-stochastic PDEs offer powerful…
In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Levy process. Our approach requires to establish a…
The search for hidden targets is a fundamental problem in many areas of science, engineering, and other fields. Studies of search processes often adopt a probabilistic framework, in which a searcher randomly explores a spatial domain for a…
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a one-dimensional parameter space, L\'evy…
A concept of quantum stochastic convolution cocycle is introduced and studied in two different contexts -- purely algebraic and operator space theoretic. A quantum stochastic convolution cocycle is a quantum stochastic process on a…
On the basis of multivariate Langevin processes we present a realization of Levy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity dependent stochastic force we…
The purpose of this paper is to study a non-convex fuzzy multi-objective quadratic programming problem, in which both the technological coefficients and resources are fuzzy with nonlinear membership function. A computational procedure to…
The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…
This paper studies system theoretic properties of the class of difference inclusions of convex processes. We will develop a framework considering eigenvalues and eigenvectors, weakly and strongly invariant cones, and a decomposition of…
A stochastic sewing lemma which is applicable for processes taking values in Banach spaces is introduced. Applications to additive functionals of fractional Brownian motion of distributional type are discussed.
Time series clustering is essential in scientific applications, yet methods for functional time series, collections of infinite-dimensional curves treated as random elements in a Hilbert space, remain underdeveloped. This work presents…
Self-similar processes are useful in modeling diverse phenomena that exhibit scaling properties. Operator scaling allows a different scale factor in each coordinate. This paper develops practical methods for modeling and simulating…
In this paper we study Fresnel pseudoprocesses whose signed measure density is a solution to a higher-order extension of the equation of vibrations of rods. We also investigate space-fractional extensions of the pseudoprocesses related to…
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…
In this paper, we introduce branching processes in a L\'evy random environment. In order to define this class of processes, we study a particular class of non-negative stochastic differential equations driven by Brownian motions and Poisson…