Constrained stochastic differential equations on smooth manifolds
Material type:
BookLanguage: en Publication details: Bangalore : IISc , 2023 .Description: xi, 96p. col. ill. ; 29.1 cm * 20.5 cm e-Thesis 3.036MbDissertation: PhD; 2023; Computational and data sciencesSubject(s): DDC classification: - 510 SUM
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JRD Tata Memorial Library | 510 SUM (Browse shelf(Opens below)) | Available | ET00182 |
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PhD; 2023; Computational and data sciences
Dynamical systems with uncertain fluctuations are usually modelled using Stochastic Differential Equations (SDEs). Due to operation and performance related conditions, these equations may also need to satisfy the constraint equations. Often the constraint equations are ``algebraic". Such constraint equations along with the given SDE form a system of Stochastic Differential-Algebraic Equations (SDAEs). The main objective of this thesis is to consider these equations on smooth manifolds. However, we first consider SDAEs on Euclidean spaces to understand these equations locally. A sufficient condition for the existence and uniqueness of the solution is obtained for SDAEs on Euclidean spaces. We also give necessary condition for the existence of the solution. Based on the necessary condition, there exists a class of SDAEs for which there is no solution. Since all SDAEs are not solvable, we present methods and algorithms to find approximate solution of the given SDAE.
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