Brownian motion on [0,∞) with linear drift, reflected at zero: exact asymptotics for ergodic means
- Faculty of Mechanics and Mathematics, Moscow State University (Russian Federation)
For the Brownian motion X{sub μ}(t) on the half-axis [0,∞) with linear drift μ, reflected at zero and for fixed numbers p>0, δ>0, d>0, a≥0, we calculate the exact asymptotics as T→∞ of the mathematical expectations and probabilities as well as of their conditional versions. For p=1 we give explicit formulae for the emerging constants via the Airy function. We consider an application of the results obtained to the problem of studying the behaviour of a Brownian particle in a gravitational field in a container bounded below by an impenetrable wall when μ=−mg/(2kT{sub K}), where m is the mass of the Brownian particle, g is the gravitational acceleration, k is the Boltzmann constant, T{sub K} is the temperature in the Kelvin scale. The analysis is conducted by the Laplace method for the sojourn time of homogeneous Markov processes. Bibliography: 31 titles. (paper)
- OSTI ID:
- 22875750
- Journal Information:
- Sbornik. Mathematics, Vol. 208, Issue 7; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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