def METHOD_NAME(ltisde_as_linearsde, ltisde, v_const, diffusion):
    out_linear_forward, _ = ltisde_as_linearsde.forward_realization(
        v_const, t=0.0, dt=0.1, _diffusion=diffusion
    )
    out_lti_forward, _ = ltisde.forward_realization(
        v_const, t=0.0, dt=0.1, _diffusion=diffusion
    )
    out_linear_forward_next, _ = ltisde_as_linearsde.forward_rv(
        out_linear_forward, t=0.1, dt=0.1, _diffusion=diffusion
    )
    out_lti_forward_next, _ = ltisde.forward_rv(
        out_lti_forward, t=0.1, dt=0.1, _diffusion=diffusion
    )
    out_linear, _ = ltisde_as_linearsde.backward_realization(
        realization_obtained=out_linear_forward_next.mean,
        rv=out_linear_forward,
        t=0.1,
        dt=0.1,
        _diffusion=diffusion,
    )
    out_lti, _ = ltisde.backward_realization(
        realization_obtained=out_lti_forward_next.mean,
        rv=out_lti_forward,
        t=0.1,
        dt=0.1,
        _diffusion=diffusion,
    )
    np.testing.assert_allclose(out_linear.mean, out_lti.mean)
    np.testing.assert_allclose(out_linear.cov, out_lti.cov, atol=1e-9)