A geometric interpretation of the transition density of a symmetric Levy process

作者：Jacob Niels^*; Knopova Victorya; Landwehr Sandra; Schilling Rene L

来源：Science China Mathematics, 2012, 55(6): 1099-1126.

DOI：10.1007/s11425-012-4368-0

• transition function estimates
• Levy processes
• metric measure spaces
• heat kernel bounds
• infinitely divisible distributions
• self-reciprocal distributions

We study for a class of symmetric L,vy processes with state space a%26quot;e (n) the transition density p (t) (x) in terms of two one-parameter families of metrics, (d (t) ) (t %26gt; 0) and (delta (t) ) (t %26gt; 0). The first family of metrics describes the diagonal term p (t) (0); it is induced by the characteristic exponent psi of the L,vy process by . The second and new family of metrics delta (t) relates to through the formula %26lt;br%26gt;[GRAPHICS] %26lt;br%26gt;where F denotes the Fourier transform. Thus we obtain the following %26quot;Gaussian%26quot; representation of the transition density: corresponds to a volume term related to and where an %26quot;exponential%26quot; decay is governed by delta (t) (2) . This gives a complete and new geometric, intrinsic interpretation of p (t) (x).

• 出版日期2012-6