Local Lipschitz Continuity In The Initial Value And Strong Completeness For Nonlinear Stochastic Differential Equations
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Local Lipschitz Continuity In The Initial Value And Strong Completeness For Nonlinear Stochastic Differential Equations
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Author : Sonja Cox
language : en
Publisher:
Release Date : 2024
Local Lipschitz Continuity In The Initial Value And Strong Completeness For Nonlinear Stochastic Differential Equations written by Sonja Cox and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Mathematics categories.
"Recently, Hairer et al. (2015) showed that there exist stochastic differential equations (SDEs) with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong Lp-sense with respect to the initial value for every p (0,]. In this article we provide conditions on the coefficient functions of the SDE and on p (0,] that are sufficient for local Lipschitz continuity in the strong Lp-sense with respect to the initial value and we establish explicit estimates for the local Lipschitz continuity constants. In particular, we prove local Lipschitz continuity in the initial value for several nonlinear stochastic ordinary and stochastic partial differential equations in the literature such as the stochastic van der Pol oscillator, Brownian dynamics, the Cox-Ingersoll-Ross processes and the Cahn-Hilliard-Cook equation. As an application of our estimates, we obtain strong completeness for several nonlinear SDEs"--
Local Lipschitz Continuity In The Initial Value And Strong Completeness For Nonlinear Stochastic Differential Equations
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Author : Sonja Cox
language : en
Publisher: American Mathematical Society
Release Date : 2024-05-15
Local Lipschitz Continuity In The Initial Value And Strong Completeness For Nonlinear Stochastic Differential Equations written by Sonja Cox and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-15 with Mathematics categories.
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Invariant Measures For Stochastic Nonlinear Schr Dinger Equations
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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2019-08-22
Invariant Measures For Stochastic Nonlinear Schr Dinger Equations written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-22 with Mathematics categories.
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
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Author : Jialin Hong
language : en
Publisher: Springer Nature
Release Date : 2023-02-21
Symplectic Integration Of Stochastic Hamiltonian Systems written by Jialin Hong and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-21 with Mathematics categories.
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
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Author : Dongxiao Yu
language : en
Publisher: American Mathematical Society
Release Date : 2024-07-25
Asymptotic Completeness For A Scalar Quasilinear Wave Equation Satisfying The Weak Null Condition written by Dongxiao Yu and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-25 with Mathematics categories.
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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
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Author : Philipp Grohs
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07
A Proof That Artificial Neural Networks Overcome The Curse Of Dimensionality In The Numerical Approximation Of Black Scholes Partial Differential Equations written by Philipp Grohs and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.
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Equivalent Definitions Of Arthur Packets For Real Classical Groups
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Author : J. Adams
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-09
Equivalent Definitions Of Arthur Packets For Real Classical Groups written by J. Adams and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Mathematics categories.
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Noncommutative Coordinates For Symplectic Representations
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Author : Daniele Alessandrini
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-09
Noncommutative Coordinates For Symplectic Representations written by Daniele Alessandrini and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Mathematics categories.
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Regularity With Respect To The Parameter Of Lyapunov Exponents For Diffeomorphisms With Dominated Splitting
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Author : Radu Saghin
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-09
Regularity With Respect To The Parameter Of Lyapunov Exponents For Diffeomorphisms With Dominated Splitting written by Radu Saghin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Mathematics categories.
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Extreme Superposition High Order Fundamental Rogue Waves In The Far Field Regime
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Author : Deniz Bilman
language : en
Publisher: American Mathematical Society
Release Date : 2024-09-09
Extreme Superposition High Order Fundamental Rogue Waves In The Far Field Regime written by Deniz Bilman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-09 with Mathematics categories.
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