On symmetries of stochastic differential equations |
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| Authors: | Roman Kozlov |
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| Affiliation: | 1. SATIE laboratory, Université Paris-Sud, Université Paris-Saclay, 91405 Orsay, France;2. VEOLIA RECHERCHE & INNOVATION, 291 av. Dreyfous Ducas, Limay, France;1. Department of Mathematics, Info Institute of Engineering, Kovilpalayam, Coimbatore - 641 107, Tamil Nadu, India;2. Department of Mathematics, KPR Institute of Engineering and Technology, Arasur, Coimbatore - 641 407, Tamil Nadu, India;3. Department of Mathematics, SRMV College of Arts and Science, Coimbatore - 641 020, Tamil Nadu, India;4. Universidad de La Laguna, Departamento de Análisis Matemático, 38271 La Laguna, Tenerife, Spain;1. Faculty of Natural Science and Technology, Hanoi Metropolitan University, Hanoi, Viet Nam;2. VNU University of Languages and International Studies, Vietnam National University, Hanoi, Viet Nam;3. Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey;4. Faculty of Information Technology, University of Technology - Logistics of Public Security, Bac Ninh, Viet Nam;1. Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2. Department of Mathematics and Statistics, The University of Dodoma, Dodoma PO. Box: 259, Tanzania;3. Department of Statistics and Financial Mathematics, Nanjing University of Science and Technology, Nanjing, Jiangsu, PR China;4. Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore 54000, Pakistan;5. College of Statistical and Actuarial Sciences, University of the Punjab Lahore, Pakistan;1. Engineering Academic Area, Autonomous University of Hidalgo State, Carr. Pachuca Tulancingo Km. 4.5, Pachuca, C.P. 42184, Mexico;2. Educational Program of Aeronautical Engineering, Metropolitan Polytechnic University of Hidalgo State, Boulevard Acceso a Tolcayuca 1009, Ex Hacienda San Javier, CP. 43860, Mexico |
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| Abstract: | This note can be considered as a supplement to article [8]. Its purpose is twofold. First, to show that symmetries of Itô stochastic differential equations form a Lie algebra. Second, to provide more precise formulation of the relation between symmetries of SDEs and symmetries of the associated Fokker–Planck equation. Relation between first integrals of SDEs and symmetries of the associated Fokker–Planck equation is also considered. |
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