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Limit theorem for continuous-time random walks with two time scales
- Source :
- Journal of Applied Probability. 41:455-466
- Publication Year :
- 2004
- Publisher :
- Cambridge University Press (CUP), 2004.
-
Abstract
- Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.
- Subjects :
- Statistics and Probability
Weak convergence
Stochastic process
Anomalous diffusion
General Mathematics
Mathematical analysis
010102 general mathematics
Random walk
01 natural sciences
010104 statistics & probability
Scaling limit
Convergence of random variables
Probability theory
0101 mathematics
Statistics, Probability and Uncertainty
Continuous-time random walk
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi.dedup.....2acb46636c0e04cb4457d12b959af1d0