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 |
| Summary: | 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. |
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| ISSN: | 2227-7390 |