Algebraic structure of stochastic expansions and efficient simulation

en

468

2144

2361

2382

2012

2012

1364-5021

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems. Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration Show moreWe investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems. Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein, we show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders. Show less

Royal Society, The

journal article

ACL

Mathématiques [math]/Mathématiques générales [math.GM]

efficient simulation
Algebraic structure
stochastic expansions

aut

International