1,721,011 research outputs found
Efficient estimators with sample observations generated by independent planar random flights
No full textOn random flights with non-uniformly distributed directions
No full textThis paper deals with a new class of random flights in a"e (d) , d >= 2, characterized by non-uniform probability distributions on the multidimensional sphere. These random motions differ from similar models appeared in literature where the directions are taken according to the uniform law. The family of angular probability distributions introduced in this paper depends on a parameter nu >= 0, which gives the anisotropy of the motion. Furthermore, we assume that the number of changes of direction performed by the random flight is fixed. The time lengths between two consecutive changes of orientation have joint probability distribution given by a Dirichlet density function. The analysis of the position (X) under bar (d) t > 0, obtained as projection onto the lower space R-m , m 0, is very complicated; nevertheless for some values of nu, we provide some explicit results about the process. Indeed, for nu=1 we get the characteristic function of the random flight moving in a"e (d) . By inverting the obtained characteristic function, we derive the analytic form (up to some constants) of the probability distribution of (X) under bar (d), t > 0. It is worth to mention that the stochastic processes considered in this paper belong to the class of the non-isotropic random walks, which has several applications in the mechanical statistics
Transport processes with random jump rate
No full textThe aim of this paper is to study transport processes with random jump rate, i.e. mixed
transport processes. We introduce and construct such processes by means of the approach
based on dynamical systems. Furthermore, if our models evolve linearly, a strong large
number law and a functional central limit theorem hol
Random flights in higher spaces
No full textWe consider in this paper random flights in R-d performed by a particle changing direction of motion at Poisson times. Directions are uniformly distributed on hyperspheres S-1(d). We obtain the conditional characteristic function of the position of the particle after n changes of direction. From this characteristic function we extract the conditional distributions in terms of (n + 1)-fold integrals of products of Bessel functions. These integrals can be worked out in simple terms for spaces of dimension d = 2 and d = 4. In these two cases also the unconditional distribution is determined in explicit form. Some distributions connected with random flights in R-3 are discussed and in some special cases are analyzed in full detail. We point out that a strict connection between these types of motions with infinite directions and the equation of damped waves holds only for d = 2. Related motions with random velocity in spaces of lower dimension are analyzed and their distributions derived
Stochastic solutions for time-fractional heat equations with complex spatial variables
No full textWe deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral oper- ator solution to the heat-type equation where the time derivative is replaced with the convolution-type generalization of the regularized Caputo derivative. We prove that this operator is solution of a complex time-fractional heat equation with com- plex spatial variable. This approach leads to a wrapped Brownian motion on a circle time-changed by the inverse of the related subordinator. This time-changed Brownian motion is analyzed and, in particular, some results on its moments, as well as its con- struction as weak limit of continuous-time random walks, are obtained. The extension of our approach to the higher dimensional case is also provided
Random motions at finite velocity in a non-Euclidean space
No full textIn this paper telegraph processes on geodesic lines of the Poincare half-space and Poincare disk are introduced and the behavior of their hyperbolic distances examined. Explicit distributions of the processes are obtained and the related governing equations derived. By means of the processes on geodesic lines, planar random motions (with independent components) in the Poincare half-space and disk are defined and their hyperbolic random distances studied. The limiting case of one-dimensional and planar motions together with their hyperbolic distances is discussed with the aim of establishing connections with the well-known stochastic representations of hyperbolic Brownian motion. Extensions of motions with finite velocity to the three-dimensional space are also hinted at, in the final section
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