Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations
Title | Local Lipschitz Continuity in the Initial Value and Strong Completeness for Nonlinear Stochastic Differential Equations PDF eBook |
Author | Sonja Cox |
Publisher | American Mathematical Society |
Pages | 102 |
Release | 2024-05-15 |
Genre | Mathematics |
ISBN | 1470467011 |
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Invariant Measures for Stochastic Nonlinear Schrödinger Equations
Title | Invariant Measures for Stochastic Nonlinear Schrödinger Equations PDF eBook |
Author | Jialin Hong |
Publisher | Springer Nature |
Pages | 220 |
Release | 2019-08-22 |
Genre | Mathematics |
ISBN | 9813290692 |
This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.
Symplectic Integration of Stochastic Hamiltonian Systems
Title | Symplectic Integration of Stochastic Hamiltonian Systems PDF eBook |
Author | Jialin Hong |
Publisher | Springer Nature |
Pages | 307 |
Release | 2023-02-21 |
Genre | Mathematics |
ISBN | 9811976708 |
This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems. The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.
Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition
Title | Asymptotic Completeness for a Scalar Quasilinear Wave Equation Satisfying the Weak Null Condition PDF eBook |
Author | Dongxiao Yu |
Publisher | American Mathematical Society |
Pages | 140 |
Release | 2024-07-25 |
Genre | Mathematics |
ISBN | 1470470489 |
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A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
Title | A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations PDF eBook |
Author | Philipp Grohs |
Publisher | American Mathematical Society |
Pages | 106 |
Release | 2023-04-07 |
Genre | Mathematics |
ISBN | 147045632X |
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Cubical Models of $(infty ,1)$-Categories
Title | Cubical Models of $(infty ,1)$-Categories PDF eBook |
Author | Brandon Doherty |
Publisher | American Mathematical Society |
Pages | 122 |
Release | 2024-06-07 |
Genre | Mathematics |
ISBN | 1470468948 |
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On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse–Weil–Artin $L$-Series
Title | On Refined Conjectures of Birch and Swinnerton-Dyer Type for Hasse–Weil–Artin $L$-Series PDF eBook |
Author | David Burns |
Publisher | American Mathematical Society |
Pages | 168 |
Release | 2024-06-07 |
Genre | Mathematics |
ISBN | 1470469669 |
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