Time fractional equations and probabilistic representation
Author
Abstract
Suggested Citation
DOI: 10.1016/j.chaos.2017.04.029
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Meerschaert, Mark M. & Scheffler, Hans-Peter, 2008. "Triangular array limits for continuous time random walks," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1606-1633, September.
- Meerschaert, Mark M. & Scheffler, Hans-Peter, 2006. "Stochastic model for ultraslow diffusion," Stochastic Processes and their Applications, Elsevier, vol. 116(9), pages 1215-1235, September.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Cho, Soobin & Kim, Panki, 2020. "Estimates on the tail probabilities of subordinators and applications to general time fractional equations," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4392-4443.
- D’Ovidio, Mirko & Loreti, Paola, 2018. "Solutions of fractional logistic equations by Euler’s numbers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 1081-1092.
- Beghin, Luisa & Cristofaro, Lorenzo & Mishura, Yuliya, 2024. "A class of processes defined in the white noise space through generalized fractional operators," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
- Mirko D’Ovidio, 2022. "On the Non-Local Boundary Value Problem from the Probabilistic Viewpoint," Mathematics, MDPI, vol. 10(21), pages 1-26, November.
- Zhang, Shuaiqi & Chen, Zhen-Qing, 2022. "Fokker–Planck equation for Feynman–Kac transform of anomalous processes," Stochastic Processes and their Applications, Elsevier, vol. 147(C), pages 300-326.
- D’Ovidio, Mirko & Iafrate, Francesco, 2024. "Elastic drifted Brownian motions and non-local boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
- Du, Qiang & Toniazzi, Lorenzo & Zhou, Zhi, 2020. "Stochastic representation of solution to nonlocal-in-time diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2058-2085.
- Ascione, Giacomo & Vidotto, Anna, 2025. "Time changed spherical Brownian motions with longitudinal drifts," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
- Meerschaert, Mark M. & Toaldo, Bruno, 2019. "Relaxation patterns and semi-Markov dynamics," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2850-2879.
- Choe, Geon Ho & Lee, Dong Min, 2016. "Numerical computation of hitting time distributions of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 289-294.
- Veillette, Mark & Taqqu, Murad S., 2010. "Using differential equations to obtain joint moments of first-passage times of increasing Lévy processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 697-705, April.
- Fernandez-Anaya, G. & Valdes-Parada, F.J. & Alvarez-Ramirez, J., 2011. "On generalized fractional Cattaneo’s equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4198-4202.
- P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
- Magdziarz, M. & Scheffler, H.P. & Straka, P. & Zebrowski, P., 2015. "Limit theorems and governing equations for Lévy walks," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4021-4038.
- Kumar, A. & Vellaisamy, P., 2015. "Inverse tempered stable subordinators," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 134-141.
- Lele Yuan & Kewei Liang & Huidi Wang, 2023. "Solving Inverse Problem of Distributed-Order Time-Fractional Diffusion Equations Using Boundary Observations and L 2 Regularization," Mathematics, MDPI, vol. 11(14), pages 1-20, July.
- D’Ovidio, Mirko, 2012. "From Sturm–Liouville problems to fractional and anomalous diffusions," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3513-3544.
- Magdziarz, Marcin, 2009. "Stochastic representation of subdiffusion processes with time-dependent drift," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3238-3252, October.
- Yu, Qiang & Turner, Ian & Liu, Fawang & Vegh, Viktor, 2022. "The application of the distributed-order time fractional Bloch model to magnetic resonance imaging," Applied Mathematics and Computation, Elsevier, vol. 427(C).
- Giacomo Ascione & Nikolai Leonenko & Enrica Pirozzi, 2022. "Non-local Solvable Birth–Death Processes," Journal of Theoretical Probability, Springer, vol. 35(2), pages 1284-1323, June.
- Kerger, Phillip & Kobayashi, Kei, 2020. "Parameter estimation for one-sided heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 164(C).
- Kondratiev, Yuri & da Silva, José L., 2023. "Compound Poisson processes: Potentials, Green measures and random times," Statistics & Probability Letters, Elsevier, vol. 197(C).
- Beghin, Luisa, 2018. "Fractional diffusion-type equations with exponential and logarithmic differential operators," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2427-2447.
- Gupta, Neha & Kumar, Arun, 2022. "Inverse tempered stable subordinators and related processes with Mellin transform," Statistics & Probability Letters, Elsevier, vol. 186(C).
- Beghin, Luisa & Macci, Claudio & Ricciuti, Costantino, 2020. "Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6364-6387.
- Torricelli, Lorenzo, 2020. "Trade duration risk in subdiffusive financial models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
- Kumar, A. & Wyłomańska, A. & Połoczański, R. & Sundar, S., 2017. "Fractional Brownian motion time-changed by gamma and inverse gamma process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 648-667.
More about this item
Keywords
Fractional-time derivative; Subordinator; Inverse subordinator; Lévy measure; Occupation measure;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:168-174. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.