Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications
This paper aims to propose a generalized fractional <i>Fokker–Planck equation</i> based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can pro...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/5/1102 |
| _version_ | 1797614877847584768 |
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| author | Reem Abdullah Aljethi Adem Kılıçman |
| author_facet | Reem Abdullah Aljethi Adem Kılıçman |
| author_sort | Reem Abdullah Aljethi |
| collection | DOAJ |
| description | This paper aims to propose a generalized fractional <i>Fokker–Planck equation</i> based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical solution is chosen to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. We model market data using a stable distribution to demonstrate the relationships between the tails and the new fractional <i>Fokker–Planck model</i>, as well as develop an R code that can be used to draw figures from real data. |
| first_indexed | 2024-03-11T07:18:29Z |
| format | Article |
| id | doaj.art-53af779df9984759a563ec1827eff3d0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:18:29Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-53af779df9984759a563ec1827eff3d02023-11-17T08:08:16ZengMDPI AGMathematics2227-73902023-02-01115110210.3390/math11051102Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial ApplicationsReem Abdullah Aljethi0Adem Kılıçman1Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11564, Saudi ArabiaDepartment of Mathematics and Statistics, University Putra Malaysia, Serdang 43400, Selangor, MalaysiaThis paper aims to propose a generalized fractional <i>Fokker–Planck equation</i> based on a stable Lévy stochastic process. To develop the general fractional equation, we will use the Lévy process rather than the Brownian motion. Due to the Lévy process, this fractional equation can provide a better description of heavy tails and skewness. The analytical solution is chosen to solve the fractional equation and is expressed using the H-function to demonstrate the indicator entropy production rate. We model market data using a stable distribution to demonstrate the relationships between the tails and the new fractional <i>Fokker–Planck model</i>, as well as develop an R code that can be used to draw figures from real data.https://www.mdpi.com/2227-7390/11/5/1102Lévy stable<i>Fokker–Planck equation</i>fractional differential equationsentropy |
| spellingShingle | Reem Abdullah Aljethi Adem Kılıçman Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications Mathematics Lévy stable <i>Fokker–Planck equation</i> fractional differential equations entropy |
| title | Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications |
| title_full | Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications |
| title_fullStr | Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications |
| title_full_unstemmed | Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications |
| title_short | Derivation of the Fractional <i>Fokker–Planck Equation</i> for Stable Lévy with Financial Applications |
| title_sort | derivation of the fractional i fokker planck equation i for stable levy with financial applications |
| topic | Lévy stable <i>Fokker–Planck equation</i> fractional differential equations entropy |
| url | https://www.mdpi.com/2227-7390/11/5/1102 |
| work_keys_str_mv | AT reemabdullahaljethi derivationofthefractionalifokkerplanckequationiforstablelevywithfinancialapplications AT ademkılıcman derivationofthefractionalifokkerplanckequationiforstablelevywithfinancialapplications |