Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations

It is shown that one can generalize the procedure of a stochastic change of time to random processes associated with fourth-order differential equations. Using this procedure, and also the obtained analog of the Girsanov–Cameron–Martin formula, we derive a formula for transforming a path integral (as an integral with respect to a quasimeasure) under path reparametrization. By means of the reparametrization formula and the formula for transforming the path integral under a homogeneous point transformation of the phase space we obtain an integral relation, expressed in terms of symbols of path integrals, between the Green's functions of two quantum-mechanical problems associated with fourth-order differential equations.