StratonovichProcess

StratonovichProcess[{a, b}, x, t] represents a Stratonovich process x(t), where dx(t) = a(t,x(t))dt + b(t,x(t)) ∘ dw(t).

• StratonovichProcess[{a, b, c}, x, t] represents a Stratonovich process y(t) = c(t,x(t)).
• StratonovichProcess[..., ..., {x, x0}, {t, t0}] represents a Stratonovich process with initial condition x(t0) = x0.
• StratonovichProcess[..., ..., ..., Σ] uses a Wiener process w(t) with covariance Σ.
• StratonovichProcess[proc] converts proc to a standard Stratonovich process whenever possible.
• StratonovichProcess[sdeqns, expr, x, t, w, dproc] represents a Stratonovich process specified by a stochastic differential equation sdeqns.

Stratonovich processes use a different stochastic calculus convention than Itô processes.

Examples

StratonovichProcess[{x[t], 1}, x[t], t]

proc = StratonovichProcess[{-x[t], x[t]}, x[t], t];
RandomFunction[proc, {0, 1, 0.01}]

StratonovichProcess[{0, x[t]}, x[t], t, {x, 1}, {t, 0}]

*See the official Wolfram Language Reference for more details.