The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise
In the present paper, we study the problem of estimating a drift parameter in stochastic evolution equations on graphs. We focus on equations driven by fractional Brownian motions, which are particularly useful e.g., in biology or neuroscience. We derive a novel estimator (the combined estimator) an...
| Published in: | Mathematics |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-10-01
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1766 |
| _version_ | 1850548281793314816 |
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| author | Pavel Kříž Leszek Szała |
| author_facet | Pavel Kříž Leszek Szała |
| author_sort | Pavel Kříž |
| collection | DOAJ |
| container_title | Mathematics |
| description | In the present paper, we study the problem of estimating a drift parameter in stochastic evolution equations on graphs. We focus on equations driven by fractional Brownian motions, which are particularly useful e.g., in biology or neuroscience. We derive a novel estimator (the combined estimator) and prove its strong consistency in the long-span asymptotic regime with a discrete-time sampling scheme. The promising performance of the combined estimator for finite samples is examined under various scenarios by Monte Carlo simulations. |
| format | Article |
| id | doaj-art-1346f005b9e1495bbdd224bf94de3c43 |
| institution | Directory of Open Access Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| spelling | doaj-art-1346f005b9e1495bbdd224bf94de3c432025-08-19T22:36:47ZengMDPI AGMathematics2227-73902020-10-01810176610.3390/math8101766The Combined Estimator for Stochastic Equations on Graphs with Fractional NoisePavel Kříž0Leszek Szała1Department of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech RepublicDepartment of Mathematics, Faculty of Chemical Engineering, University of Chemistry and Technology Prague, 16628 Prague, Czech RepublicIn the present paper, we study the problem of estimating a drift parameter in stochastic evolution equations on graphs. We focus on equations driven by fractional Brownian motions, which are particularly useful e.g., in biology or neuroscience. We derive a novel estimator (the combined estimator) and prove its strong consistency in the long-span asymptotic regime with a discrete-time sampling scheme. The promising performance of the combined estimator for finite samples is examined under various scenarios by Monte Carlo simulations.https://www.mdpi.com/2227-7390/8/10/1766stochastic equations on graphsfractional Brownian motionparameter estimation |
| spellingShingle | Pavel Kříž Leszek Szała The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise stochastic equations on graphs fractional Brownian motion parameter estimation |
| title | The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise |
| title_full | The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise |
| title_fullStr | The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise |
| title_full_unstemmed | The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise |
| title_short | The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise |
| title_sort | combined estimator for stochastic equations on graphs with fractional noise |
| topic | stochastic equations on graphs fractional Brownian motion parameter estimation |
| url | https://www.mdpi.com/2227-7390/8/10/1766 |
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