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Support Stochastic Integration #1004

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@juan-g-bonilla

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@juan-g-bonilla

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A lot of real physical processes are stochastic in nature: their evolution is not deterministic but randomly evolving (as far as a reasonable observer can tell).

An example of this is the Total Solar Irradiance (TSI) (which affects solar radiation pressure):
Image

Another is the atmospheric conditions (mainly winds and density) which are driven by the solar flux index and geomagnetic activity index (both random):
Image

Thrusters also tend to produce non-constant non-ideal thrust profiles, which can be seen as stochastic processes.

Finally, stochastic (random) disturbance forces or torques can also be included to account for the residual effects that are not modeled through deterministic dynamics.

The dynamics of a stochastic dynamical system are given by:

dx = f(t,x)dt + sum_i g_i(t,x) dW_i

where f(t,x) is the deterministic term (also called drift, the only term in ODEs) and g_i are the diffusion terms (which map the contribution of the random process W_i to the dynamics).

To model such systems, we'd need to:

  • modify the state machinery to support setting the diffusion of a state (not only its drift/derivative) for multiple noise sources
  • modify DynamicObject to compute g_i, not only f
  • implement stochastic integrators

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