Limit theorems for a Brownian motion with drift in a white noise environment
β Scribed by Hiroshi Tanaka
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 539 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0960-0779
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β¦ Synopsis
This paper discusses limit theorems for a diffusion analogue of Kesten-Kozlov-Spitzer's random walk in a random environment. The results obtained are similar to theirs but can be presented in a more explicit form by the use of Krein's spectral theory for one-dimensional generalized second-order differential operators of the form d/dMd/dx.
π SIMILAR VOLUMES
Let Xt be a standard d-dimensional Brownian motion with drift c started at a ΓΏxed X0, and let T be the hitting time for a sphere or concentric spherical shell. By using an appropriate martingale, a Laplace-Gegenbauer transform of the joint distribution of T and XT is determined.
Although the shakedown theorems for perfect plasticity have been known since Koiter's 1960 review paper, extensions of the theory to situations where ratchetting or reverse plasticity occurs in excess of shakedown have not appeared in the literature. In this paper a generalisation of the upper bound