A Semi-Deterministic Random Walk with Resetting
We consider a discrete-time random walk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo><...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-06-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/23/7/825 |
| _version_ | 1797411559970963456 |
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| author | Javier Villarroel Miquel Montero Juan Antonio Vega |
| author_facet | Javier Villarroel Miquel Montero Juan Antonio Vega |
| author_sort | Javier Villarroel |
| collection | DOAJ |
| description | We consider a discrete-time random walk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">Pr</mo><mfenced separators="" open="(" close=")"><msub><mi>x</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>|</mo></mrow><msub><mi>x</mi><mi>t</mi></msub><mo>=</mo><mi>n</mi></mfenced><mo>,</mo><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined. |
| first_indexed | 2024-03-09T04:46:53Z |
| format | Article |
| id | doaj.art-6659c93350b54a6190277604f332f516 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T04:46:53Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6659c93350b54a6190277604f332f5162023-12-03T13:14:11ZengMDPI AGEntropy1099-43002021-06-0123782510.3390/e23070825A Semi-Deterministic Random Walk with ResettingJavier Villarroel0Miquel Montero1Juan Antonio Vega2Instituto Universitario Física y Matemáticas University of Salamanca, Plaza Merced s/n, 37008 Salamanca, SpainDepartament de Física de Matèria Condensada, University of Barcelona, Martí i Franquès 1, E-08028 Barcelona, SpainInstituto Universitario Física y Matemáticas University of Salamanca, Plaza Merced s/n, 37008 Salamanca, SpainWe consider a discrete-time random walk <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><msub><mi>x</mi><mi>t</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> which, at random times, is reset to the starting position and performs a deterministic motion between them. We show that the quantity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">Pr</mo><mfenced separators="" open="(" close=")"><msub><mi>x</mi><mrow><mi>t</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>|</mo></mrow><msub><mi>x</mi><mi>t</mi></msub><mo>=</mo><mi>n</mi></mfenced><mo>,</mo><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula> determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined.https://www.mdpi.com/1099-4300/23/7/825random walk with resettingescape probabilitiesexit times |
| spellingShingle | Javier Villarroel Miquel Montero Juan Antonio Vega A Semi-Deterministic Random Walk with Resetting Entropy random walk with resetting escape probabilities exit times |
| title | A Semi-Deterministic Random Walk with Resetting |
| title_full | A Semi-Deterministic Random Walk with Resetting |
| title_fullStr | A Semi-Deterministic Random Walk with Resetting |
| title_full_unstemmed | A Semi-Deterministic Random Walk with Resetting |
| title_short | A Semi-Deterministic Random Walk with Resetting |
| title_sort | semi deterministic random walk with resetting |
| topic | random walk with resetting escape probabilities exit times |
| url | https://www.mdpi.com/1099-4300/23/7/825 |
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