Isaak, Elena: Solving SODEs with large noise by balanced integration methods. 2018
Inhalt
- Introduction
- 1 Balanced integration methods
- 1.1 Problem setting and general assumptions
- 1.2 Transformed Wiener noise
- 1.3 Hölder continuity of the solution
- 1.4 A simple balanced method
- 1.5 Modified solution operator
- 1.6 Reformulation of the linear integral equation
- 1.7 Balanced shift noise Euler-type methods
- 2 Numerical analysis of the balanced shift noise methods
- 2.1 Stochastic B-consistency and C-stability
- 2.2 Stochastic B-consistency and C-stability of the BSNE Euler-type method
- 2.3 Stochastic B-consistency and C-stability of the BSNI Euler-type scheme
- 3 Nonlinearity in the drift term
- 3.1 Assumptions and main results
- 3.2 Solution estimates for nonlinear equations under one-sided Lipschitz conditions
- 3.3 Reformulation of the nonlinear integral equation
- 3.4 Stochastic C-stability and B-consistency of the PBSNE method
- 3.5 Stochastic C-stability and B-consistency of the SSBSNI method
- 4 Balanced higher order methods
- 4.1 Projected balanced shift noise Milstein-type method
- 4.2 The classical balanced Milstein method
- 4.3 Preliminaries
- 4.4 C-stability of the projected balanced Milstein method
- 4.5 B-consistency of the projected balanced Milstein method
- 5 Numerical results
- A Appendix