Stochastic representation of solution to nonlocal-in-time diffusion
Du, Qiang ; Toniazzi, Lorenzo ; Zhou, Zhi
arXiv, 1810.08788 / Harvested from arXiv
Text on arXiv
The aim of this paper is to give a stochastic representation for the solution to a natural extension of the Caputo-type evolution equation. The nonlocal-in-time operator is defined by a hypersingular integral with a (possibly time-dependent) kernel function, and it results in a model which serves a bridge between normal diffusion and anomalous diffusion. We derive the stochastic representation for the weak solution of the nonlocal-in-time problem in case of nonsmooth data. We do so by starting from an auxiliary Caputo-type evolution equation with a specific forcing term. Numerical simulations are also provided to support our theoretical results.
Publié le : 2018-10-20
Classification:  Mathematics - Analysis of PDEs 
@article{1810.08788,
     author = {Du, Qiang and Toniazzi, Lorenzo and Zhou, Zhi},
     title = {Stochastic representation of solution to nonlocal-in-time diffusion},
     journal = {arXiv},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1810.08788}
}

Du, Qiang; Toniazzi, Lorenzo; Zhou, Zhi. Stochastic representation of solution to nonlocal-in-time diffusion. arXiv, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/1810.08788/