nssvie.SVIE#

class nssvie.SVIE(f, kernel_1, kernel_2, T=1.0)[source]#

Generate a stochastic Volterra integral equation

(1)#\[X_t = f(t) + \int\limits_0^t k_1(s,t) X_s \ ds + \int\limits_0^t k_2(s,t) X_s \ dB_s \qquad t \in [0,T),\]

where \(X_t\) is an unknown stochastic process, \(B_t\) the Brownian motion,

\[\int\limits_0^t k_2(s,t) X_s \ dB_s\]

is the Itô-integral and \(f \in L^2([0,T))\) and \(k_1, \ k_2 \in L^2([0,T) \times [0,T))\).

Parameters
fcallable

Function \(f\) in (1).

kernel_1, kernel_2callable

The kernels \(k_1\) and \(k_2\) in (1).

Tfloat, default 1.0

The right hand side of the interval \([0,T)\).

Methods

solve_numerical([m, solve_method])

Compute a numerical solution for the given stochastic Volterra integral equation.