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What is Heston's equation?

This paper mentions the elliptic Heston operator: $Av:= -\frac y2(v_{xx}+2\rho\sigma v_{xy} + \sigma^2v_{yy}) - (c_0 - q - \frac y2)v_x + \kappa(\theta -y)v_y + c_0v$. Then boundary value problem ...