A Lie algebraic approach to numerical integration of stochastic differential equations

SIAM Journal on Scientific Computing

Volumn 23, Issue 3, 2002, Pages 866-890

  Misawa, Tetsuya ^a  

^a NAGOYA CITY UNIVERSITY   (Japan)

Author keywords

Composition methods (operator splitting method); Lie algebra; Mathematical finance; Stochastic differential equations; Stochastic Hamiltonian dynamical systems; Stochastic nonlinear system

Indexed keywords

ALGEBRA; APPROXIMATION THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; HAMILTONIANS; INTEGRATION; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; RANDOM PROCESSES;

STOCHASTIC DIFFERENTIAL EQUATIONS (SDE);

COMPUTATIONAL METHODS;

EID: 0036289720     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S106482750037024X     Document Type: Article

References (26)

1. Flots et series de Taylor stochastiqes
2. High strong methods for non-commutative stochastic ordinary differential equation systems and the magnus formula
3. Order conditions of stochastic Runge-kutta methods by B-series
4. Asymptotic expansion of stochastic flows
5. Fourth-order symplectic integration
6. Bessel processes, asian options and perpetuities
7. Conservative numerical methods for ẍ = f(x)
8. Composite methods for numerical solution of stiff systems of ODE's
9. Explicit energy conservative difference schemes for nonlinear dynamical systems with at most quartic potentials
10. A survey of numerical methods for stochastic differential equations
11. On the representation of solutions of stochastic differential equations
12. Asymptotic self-similarity and short time asymptotics of stochastic flows
13. Algebraic structure of multiple stochastic integrals with respect to Brawnian motions and Poisson processes
14. On the numerical integration of ordinary differential equations by symmetric composition methods
15. Conserved quantities and symmetries related to stochastic dynamical systems
16. Energy conservative stochastic difference scheme for stochastic Hamilton dynamical systems
17. A lie algebraic approach to dynamical system prediction
18. Simulation of stochastic differential equations
19. General theory of higher-order exponential product formulas
20. A difference method of solution in the case of the multidimensional equation of heat conduction
21. Construction of higher order symplectic integrators