Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation
A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/668 |
| _version_ | 1797569463902535680 |
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| author | Johan Anderson |
| author_facet | Johan Anderson |
| author_sort | Johan Anderson |
| collection | DOAJ |
| description | A novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker–Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality (<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>) of the stable Lévy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> is computed. |
| first_indexed | 2024-03-10T20:11:59Z |
| format | Article |
| id | doaj.art-fc16448491d74643912aec760099de91 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:11:59Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-fc16448491d74643912aec760099de912023-11-19T22:54:31ZengMDPI AGMathematics2227-73902020-04-018566810.3390/math8050668Information Geometric Investigation of Solutions to the Fractional Fokker–Planck EquationJohan Anderson0Department of Space, Earth and Environment, Chalmers University of Technology, SE-412 96 Göteborg, SwedenA novel method for measuring distances between statistical states as represented by probability distribution functions (PDF) has been proposed, namely the information length. The information length enables the computation of the total number of statistically different states that a system evolves through in time. Anomalous transport can presumably be modeled fractional velocity derivatives and Langevin dynamics in a Fractional Fokker–Planck (FFP) approach. The numerical solutions or PDFs are found for varying degree of fractionality (<inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula>) of the stable Lévy distribution as solutions to the FFP equation. Specifically, the information length of time-dependent PDFs for a given fractional index <inline-formula> <math display="inline"> <semantics> <mi>α</mi> </semantics> </math> </inline-formula> is computed.https://www.mdpi.com/2227-7390/8/5/668information geometryfractional Fokker–Planck equationanomalous transport |
| spellingShingle | Johan Anderson Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation Mathematics information geometry fractional Fokker–Planck equation anomalous transport |
| title | Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation |
| title_full | Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation |
| title_fullStr | Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation |
| title_full_unstemmed | Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation |
| title_short | Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation |
| title_sort | information geometric investigation of solutions to the fractional fokker planck equation |
| topic | information geometry fractional Fokker–Planck equation anomalous transport |
| url | https://www.mdpi.com/2227-7390/8/5/668 |
| work_keys_str_mv | AT johananderson informationgeometricinvestigationofsolutionstothefractionalfokkerplanckequation |