Lévy Stable Processes . from Stationary to Self - Similar Dynamics and Back . an Application to Finance ∗
نویسندگان
چکیده
We employ an ergodic theory argument to demonstrate the foundations of ubiquity of Lévy stable self-similar processes in physics and present a class of models for anomalous and nonextensive diffusion. A relationship between stationary and self-similar models is clarified. The presented stochastic integral description of all Lévy stable processes could provide new insights into the mechanism underlying a range of self-similar natural phenomena. Finally, this effect is illustrated by self-similar approach to financial modelling.
منابع مشابه
Maharam extension and stationary stable processes
We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences. 1. Introduction. In a fundamental paper [9], Rosi´nski revealed the hidden structure of stationary symmetric α-stable (SαS) processes. Namely, he proved t...
متن کاملDiscrete approximation of a stable self-similar stationary increments process
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known about the context in which such processes can arise. To our knowledge, discretization and convergence theorems are available only in the case of stable Lévy motions and fra...
متن کاملConditioned stable Lévy processes and Lamperti representation . February 2 , 2008
By killing a stable Lévy process when it leaves the positive half-line, or by conditioning it to stay positive, or by conditioning it to hit 0 continuously, we obtain three different positive self-similar Markov processes which illustrate the three classes described by Lamperti [10]. For each of these processes, we compute explicitly the infinitesimal generator from which we deduce the characte...
متن کاملEstimation of stable CARMA models with an application to electricity spot prices
We discuss theoretical properties and estimation of continuous-time ARMA (CARMA) processes, which are driven by a stable Lévy process. Such processes are very useful in a continuous-time linear stationary set-up: they have a similar structure as the widely used ARMA models, and provide all advantages of a continuous-time model. As an application we consider data from a deregulated electricity m...
متن کاملFunctional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows
We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying Lévy measures. The limit process is a new class of symmetric stable self-similar processes with stationary increments, that coincides, on a part of its parameter space, with a previously described process. The normalizing sequence an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012