Feller Fractional Diiusion and L Evy Stable Motions

نویسنده

  • Rudolf GORENFLO
چکیده

{ Fractional calculus allows to generalize the standard (linear and one dimensional) diiusion equation by replacing the second-order space derivative by a derivative of fractional order. If this is taken as the pseudo-diierential operator introduced by Feller in 1952 the fundamental solution of the resulting diiusion equation is a probability density evolving in time and stable in the sense of L evy. Like the standard diiusion equation through its fundamental solution, the Gaussian density, yields the well-known Brownian motion, so the Feller diiusion equation yields the so called L evy stable motions, whose increments are independent and stably distributed. We show how to approximate each of these motions by a discrete-time, discrete-space random walk model, which is based on an integer-valued random variable lying in the domain of attraction of the corresponding L evy probability distribution.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Random Walk Models for Space-fractional Diiusion Processes Random Walk Models for Space-fractional Diiusion Processes

By space-fractional (or L evy-Feller) diiusion processes we mean the processes governed by a generalized diiusion equation which generates all L evy stable probability distributions with index (0 < 2), including the two symmetric most popular laws, Cauchy (= 1) and Gauss (= 2). This generalized equation is obtained from the standard linear diiusion equation by replacing the second-order space d...

متن کامل

Heavy-traffic Theory for the Heavy-tailed M/g/1 Queue and V-stable L'evy Noise Traffic Heavy-traac Theory for the Heavy-tailed M/g/1 Queue and -stable L Evy Noise Traac

The workload vt of an M/G/1 model with traac a < 1 is analyzed for the case with heavy-tailed message length distributions B(), e.g. 1 ? B() = O(?); ! 1; 1 < 2. It is shown that a factor (a) exists with (a) # 0 for a "1 such that, whenever vt is scaled by (a) and time t by 1(a) = (a)(1 ?a) then w(a) = (a)v = 1 (a) converges in distribution for a "1 and every > 0. Proper scaling of the traac loa...

متن کامل

Stable Distribution and [0;2] Power Law Dependence of Acoustic Absorption on Frequency in Various Lossy Media

Absorption of acoustic wave propagation in a large variety of lossy media is characterized by an empirical power law function of frequency, 0j!j y . It has long been noted that the exponent y ranges from 0 to 2 for diverse media. Recently, the present author [J. Acoust. Soc. Am. 115 (2004) 1424] developed a fractional Laplacian wave equation to accurately model the power law dissipation, which ...

متن کامل

Evy - Driven and Fractionally Integrated Armaprocesses with Continuous Time Parameterpeter

The deenition and properties of L evy-driven CARMA (continuous-time ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion. The use of more general L evy processes permits the speciication of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus-sian. Non-negative...

متن کامل

Evy Driven and Fractionally Integrated Arma Processes with Continuous Time Parameter

The de nition and properties of L evy driven CARMA continuous time ARMA processes are re viewed Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion The use of more general L evy processes permits the speci cation of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus sian Non negative CAR...

متن کامل

ذخیره 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 1999