<P ALIGN=RIGHT><FONT SIZE=+4>42</FONT><P>
<P>
<H1>The various linear fractional L&#233;vy motions</H1>
<P><STRONG>Gennady Samorodnitsky
 <BR> Murad S. Taqqu</STRONG><P>
<P>
<H3>Abstract:</H3>
<EM>We treat in this paper a problem raised by Cambanis and Maejima (1988). 
Linear Fractional L&#233;vy motions are <IMG  ALIGN=BOTTOM ALT="" SRC="img1.gif">-stable self-similar processes 
with stationary increments and 
 a ``moving average'' representation. The 
representation involves two real parameters <b>a</b> and <b>b</b>. When <IMG  ALIGN=BOTTOM ALT="" SRC="img2.gif">, 
the processes are identical to the Gaussian Fractional Brownian motion for all
 values of <b>a</b> and <b>b</b>. We will 
 show that different values of the parameters <b>a</b> and <b>b</b> yield different
 processes when <IMG  ALIGN=MIDDLE ALT="" SRC="img3.gif"> and when the skewness intensity is not 
necessarily zero.
</EM><P>


</BODY>