Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics. (English. Russian original) Zbl 1193.60046
Theory Probab. Appl. 53, No. 4, 594-609 (2009); translation from Teor. Veroyatn. Primen. 53, No. 4, 684-703 (2008).
Author’s abstract: Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent. The limiting anomalous diffusion is described in terms of fractional dynamics. Probabilistic interpretation of generalized fractional evolution is given in terms of the random time change (subordination) by means of hitting times processes.
Reviewer: Allan Gut (Uppsala)
MSC:
60F17 | Functional limit theorems; invariance principles |
60G50 | Sums of independent random variables; random walks |
60G22 | Fractional processes, including fractional Brownian motion |