On harmonic functions of symmetric Lévy processes. (English. French summary) Zbl 1298.60054
The author considers subordinate Brownian motions \(X_t:= B(S_t)\) such that:
- (i)
- The Brownian motion \(B\) and the subordinator \(S\) are independent.
- (ii)
- The Lévy and potential measures of \(S\) have decreasing densities.
- (iii)
- The Laplace exponent \(\phi(\lambda):=-\log(\operatorname{E} e^{-\lambda S_1})\) of \(S\) satisfies \[ \lim_{\lambda\to +\infty} \frac{\phi'(\lambda x)}{\phi'(\lambda)} = x^{\alpha/2 -1} \quad (x>0) \] for some \(\alpha\in [0,2]\).
Reviewer: Mohamed Hmissi (Tunis)
MSC:
60G51 | Processes with independent increments; Lévy processes |
60J45 | Probabilistic potential theory |
60J75 | Jump processes (MSC2010) |
60J25 | Continuous-time Markov processes on general state spaces |
Keywords:
geometric stable process; Green function; harmonic function; Lévy process; modulus of continuity; subordinator; subordinate Brownian motionReferences:
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