Inert drift system in a viscous fluid: Steady state asymptotics and exponential ergodicity
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- by Sayan Banerjee and Brendan Brown PDF
- Trans. Amer. Math. Soc. 373 (2020), 6369-6409 Request permission
Abstract:
We analyze a system of stochastic differential equations describing the joint motion of a massive (inert) particle in a viscous fluid in the presence of a gravitational field and a Brownian particle impinging on it from below, which transfers momentum proportional to the local time of collisions. We study the long-time fluctuations of the velocity of the inert particle and the gap between the two particles, and we show convergence in total variation to the stationary distribution is exponentially fast. We also produce matching upper and lower bounds on the tails of the stationary distribution and show how these bounds depend on the system parameters. A renewal structure for the process is established, which is the key technical tool in proving the mentioned results.References
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Additional Information
- Sayan Banerjee
- Affiliation: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599-3260
- MR Author ID: 1029581
- Email: sayan@email.unc.edu
- Brendan Brown
- Affiliation: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, North Carolina 27599-3260
- Email: bb@live.unc.edu
- Received by editor(s): May 28, 2019
- Received by editor(s) in revised form: January 2, 2020
- Published electronically: July 3, 2020
- Additional Notes: The first author was partially supported by a Junior Faculty Development Grant made by UNC, Chapel Hill.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 6369-6409
- MSC (2010): Primary 60J60, 60K05; Secondary 60J55, 60H20
- DOI: https://doi.org/10.1090/tran/8098
- MathSciNet review: 4155180