Mathematics – Probability
Scientific paper
2011-10-02
Mathematics
Probability
12 pages, 1 figure
Scientific paper
Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous diffusion have been observed in physics, hydrology, biology, and finance, among many other fields. Continuous-time random walks (CTRWs), introduced by Montroll and Weiss, serve as models for anomalous diffusion. CTRWs generalize the usual random walk model by allowing random waiting times between successive random jumps. Under certain conditions on the jumps and waiting times, scaled CTRWs can be shown to converge in distribution to a limit process M(t) in the cadlag space D[0,infinity) with the Skorohod J_1 or M_1 topology. An interesting question is whether stochastic integrals driven by the scaled CTRWs X^n(t) converge in distribution to a stochastic integral driven by the CTRW limit process M(t). We prove weak convergence of the stochastic integrals driven by CTRWs for certain classes of CTRWs, when the CTRW limit process is an alpha-stable Levy motion and when the CTRW limit process is a time-changed Brownian motion.
No associations
LandOfFree
Weak convergence of stochastic integrals driven by continuous-time random walks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Weak convergence of stochastic integrals driven by continuous-time random walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weak convergence of stochastic integrals driven by continuous-time random walks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-285833