Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods

Figure 1

Numerical sample paths of “$p$” of a stochastic harmonic oscillator system (SHOS) via Euler scheme, Composition 1 (Scheme 6) and Composition 2 (Scheme 5) ($dt$ = 0.05, sigma = 0.2).