[图书][B] Random Ordinary Differential Equations
X Han, PE Kloeden, X Han, PE Kloeden - 2017 - Springer
Existence and uniqueness theorems are given for RODEs under classical and Carathéodory
assumptions. In the latter case the measurability of solutions is also established. Conditions …
assumptions. In the latter case the measurability of solutions is also established. Conditions …
Runge–Kutta methods for the strong approximation of solutions of stochastic differential equations
A Rößler - SIAM Journal on Numerical Analysis, 2010 - SIAM
Some new stochastic Runge–Kutta (SRK) methods for the strong approximation of solutions
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …
of stochastic differential equations (SDEs) with improved efficiency are introduced. Their …
Ramification of rough paths
M Gubinelli - Journal of Differential Equations, 2010 - Elsevier
The stack of iterated integrals of a path is embedded in a larger algebraic structure where
iterated integrals are indexed by decorated rooted trees and where an extended Chen's …
iterated integrals are indexed by decorated rooted trees and where an extended Chen's …
The numerical approximation of stochastic partial differential equations
A Jentzen, PE Kloeden - Milan Journal of Mathematics, 2009 - Springer
The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …
development roughly similar to that of stochastic ordinary differential equations (SODEs) in …
Second order Runge–Kutta methods for Itô stochastic differential equations
A Rößler - SIAM Journal on Numerical Analysis, 2009 - SIAM
A new class of stochastic Runge–Kutta methods for the weak approximation of the solution
of Itô stochastic differential equation systems with a multidimensional Wiener process is …
of Itô stochastic differential equation systems with a multidimensional Wiener process is …
Taylor expansions of solutions of stochastic partial differential equations with additive noise
The solution of a parabolic stochastic partial differential equation (SPDE) driven by an
infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does …
infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does …
Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
We derive a new methodology for the construction of high-order integrators for sampling the
invariant measure of ergodic stochastic differential equations with dynamics constrained on …
invariant measure of ergodic stochastic differential equations with dynamics constrained on …
Runge–Kutta methods for Itô stochastic differential equations with scalar noise
A Rössler - BIT Numerical Mathematics, 2006 - Springer
A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation
systems wrt a one-dimensional Wiener process is introduced. The colored rooted tree …
systems wrt a one-dimensional Wiener process is introduced. The colored rooted tree …
Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations
E Bronasco, A Laurent - arXiv preprint arXiv:2407.07451, 2024 - arxiv.org
While backward error analysis does not generalise straightforwardly to the strong and weak
approximation of stochastic differential equations, it extends for the sampling of ergodic …
approximation of stochastic differential equations, it extends for the sampling of ergodic …
Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients
S Gan, Y He, X Wang - Applied Numerical Mathematics, 2020 - Elsevier
Traditional explicit schemes such as the Euler-Maruyama, Milstein and stochastic Runge-
Kutta methods, in general, result in strong and weak divergence when solving stochastic …
Kutta methods, in general, result in strong and weak divergence when solving stochastic …