Estimates on the Transition Densities of Girsanov Transforms of Symmetric Stable Processes

Renming Song ()
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Renming Song: University of Illinois

Journal of Theoretical Probability, 2006, vol. 19, issue 2, 487-507

Abstract: In this paper, we first study a purely discontinuous Girsanov transform which is more general than that studied in Chen and Song [(2003), J. Funct. Anal. 201, 262–281]. Then we show that the transition density of any purely discontinuous Girsanov transform of a symmetric stable process is comparable to the transition density of the symmetric stable process. The same is true for the Girsanov transform introduced in Chen and Zhang [(2002), Ann. Inst. Henri poincaré 38, 475–505]. As an application of these results, we show that the Green function of Feynman–Kac type transforms of symmetric stable processes by continuous additive functionals of zero energy, when exists, is comparable to that of the symmetric stable process.

Keywords: Transition density; Green function; Girsanov transform; Dirichlet forms; symmetric Markov processes; martingale additive functionals; additive functionals of zero energy; Feynman–Kac semigroups; symmetric stable processes; Brownian motion; Primary 60J45; Primary 60J40; Secondary 35J10; Secondary 47J20 (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10959-006-0023-4

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