ajdmom.ito_cond2_mom.int_e_poly

ajdmom.ito_cond2_mom.int_e_poly(coef, tp, m, poly)[source]

integral of \(coef \times tp \times \int_0^t e^{mks} poly ds\)

Parameters:

  • coef (fractions.Fraction) – coefficient to multiply with

  • tp (int) –

    type of the multiplication,

    tp

    multiply with

    1

    \(v_0-\theta\)

    2

    \(\theta\)

    3

    \(\sigma_v\)

  • m (int) – power of \(e^{ks}\) in the integrand

  • poly (Poly) – a Poly object, such as \(\mathbb{E}[I\!E_t^{n_1} I_t^{n_2} I_t^{*n_3} |v_0, z(s), 0\le s\le t]\), with attribute keyfor = (‘e^{kt}’, ‘t’, ‘k^{-}’, ‘v0-theta’, ‘theta’, ‘sigma’, ‘l_{1:n}’, ‘o_{1:n}’)

Returns:

a Poly with the same keyfor of the input poly

Return type:

Poly