## A formula on scattering length of dual Markov processes

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## Abstract:

A formula on the scattering length for 3-dimensional Brownian motion was conjectured by M. Kac and proved by others later. It was recently proved under the framework of symmetric Markov processes by Takeda. In this paper, we shall prove that this formula holds for Markov processes under weak duality by the machinery developed mainly by Fitzsimmons and Getoor.## References

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## Additional Information

**Ping He**- Affiliation: Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, People’s Republic of China
- Email: pinghe@mail.shufe.edu.cn
- Received by editor(s): March 2, 2010
- Received by editor(s) in revised form: May 26, 2010
- Published electronically: November 1, 2010
- Additional Notes: This research supported in part by the National Natural Science Foundation of China (Grant No. 10771131)
- Communicated by: Richard C. Bradley
- © Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**139**(2011), 1871-1877 - MSC (2010): Primary 60J40; Secondary 60J45
- DOI: https://doi.org/10.1090/S0002-9939-2010-10618-4
- MathSciNet review: 2763774