Splitting integrators for stochastic Lie–Poisson systems

• . We study stochastic Poisson integrators for a class of stochastic Poisson systems driven by Stratonovich noise. Such geometric integrators preserve Casimir functions and the Poisson map property. For this purpose, we propose explicit stochastic Poisson integrators based on a splitting strategy, and analyse their qualitative and quantitative properties: preservation of Casimir functions, existence of almost sure or moment bounds, asymptotic preserving property, and strong and weak rates of convergence. The construction of the schemes and the theoretical results are illustrated through extensive numerical experiments for three examples of stochastic Lie-Poisson systems, namely: stochastically perturbed Maxwell-Bloch, rigid body and sine-Euler equations.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Stochastic Poisson systems

splitting schemes

Poisson integrators

strong and weak rates of convergence

asymptotic preserving schemes

Maxwell-Bloch equations

rigid body equations

sine-Euler equations

sine-Euler equations

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