Electrostatic lower hybrid ’’pump’’ waves are often launched into tokamak plasmas by structures (e.g., waveguides) whose dimensions are considerably smaller than characteristic plasma sizes. Such waves propagate in well‐defined resonance cones and give rise to parametric instabilities driven by electron E×B velocities. The finite size of the resonance cone region determines the threshold for both convective quasi‐mode decay instabilities and absolute instabilities. The excitation of absolute instabilities depends on whether a traveling or standing wave pump model is used; traveling wave pumps require the daughter waves to have a definite frequency shift. Altogether, parametric instabilities driven by E×B velocities occur for threshold fields significantly below the threshold for filamentation instabilities driven by pondermotive forces. Applications to tokamak heating show that nonlinear effects set in when a certain power‐per‐wave‐launching port is exceeded. For sufficiently high powers, these instabilities will occur in the low‐density edge region of a tokamak. They are characterized by a daughter wave frequency 10% below the pump wave frequency, in agreement with experimental observations.