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#sde_solve ###a tiny library for numerically solving stochastic differential equations

##Installation

  • Clone this repo
  • enter the resulting directory
  • sudo python setup.py install or python setup.py install --user if you don't have superuser privileges.

##Use The purpose of this library is to produce numerical solutions to differential equations of the form:

d_rho = det_f(t,rho) dt + stoc_f(t, rho) dW

using the order-1.5 strong solver for non-autonomous equations from Kloeden and Platen, page 379.

There's only one function in this repo, sde_platen_15:

sde_platen_15(rho_init, det_f, stoc_f, times, dWs, e_cb)

The input variables are:

  • rho_init: an initial value. This can be any object that supports arithmetic methods in principle, but it must be accepted as input by det_f and stoc_f, see below.
  • det_f: the deterministic contribution to the derivative. This is a function with signature det_f(t, rho)
  • stoc_f: the stochastic contribution to the derivative. This is a function with signature stoc_f(t, rho).
  • times: values of time (in arb. units) at which the solution is to be calculated. In principle, can be any type which supports __getitem__. In practice, NumPy arrays work best. Note: As of the current version, sde_platen_15 assumes this iterable to have a fixed difference.
  • dWs: iterable of values for the Wiener increment. This is not generated within the function, since it is often convenient for this variable to be in scope where sde_platen_15 is called.
  • e_cb: Callback function with signature e_cb(t, rho, dW). This brings the interim values of time, solution and Wiener increment into whatever namespace in which e_cb is def'd.

##Example Coming soon

##Future Work

  • Adaptive timesteps
  • Switching the whole thing over to Julia, so I can decide at runtime whether to use an implicit method.