Upcrossings of the random walk
β Scribed by D. P. Johnson
- Publisher
- Akadmiai Kiad
- Year
- 1991
- Tongue
- English
- Weight
- 79 KB
- Volume
- 57
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Crack propagation is considered as a random walk process of consecutive atomic bond breaking and healing steps. The total number of steps is propo~ion~ to tfre propa~t~n time, and the difference of the number of breaking and healing steps is propo~ional to the location of the crack tip at that time.
The solution of the one-dimensional persistent, biased random walk is found. Its finite differences equation is derived and shown to be satisfied by the said solution.
We consider simple branching random walk, i.e., a Galton-Watson process in which each particle, as it is created, may randomly perform a unit step to the left or right. We show that for a supercritical BRW, the set of occupied points is eventually an interval. In addition, we give a limit law for t