Is it possible for the solution of the Fokker-Planck equation to have negative values? I am referring to the mathematical aspect, irrespective of its physical interpretation. Additionally, considering that the solution represents a probability distribution function, is it acceptable to impose a constraint ensuring that the solution remains strictly positive?
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In the context of quantum physics, one can derive Fokker-Planck equations for phase space distributions such as the Wigner function. Wigner functions can have regions where they are negative. – flippiefanus Dec 27 '23 at 04:04
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I think Pawla's theorem ensures that the solution of a Fokker-Planck is non-negative.
Sure, when solving the Fokker-Planck equation, both numerically and analytically, it is a usual practice to demand solutions that can be normalized and that are non-negative.
Javi
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The Fokker-Planck equation (FPE) describes the time-evolution of a probability distribution. Since (classical) probability distributions are bound to the interval $[0,1]$ (i.e., it is non-negative), then it must follow that the solution to the FPE must also remain non-negative.
Any method one uses for solving the FPE, numerically or analytically, must enforce the constraint that $p(x)>0\,\forall x$.
Kyle Kanos
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