Geodesic
Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 17-31

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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. 
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     author = {S. N. Storchak},
     title = {Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {17--31},
     publisher = {mathdoc},
     volume = {93},
     number = {1},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a1/}
}
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S. N. Storchak. Homogeneous point transformation and reparametrization of paths in path integrals for fourth-order differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 1, pp. 17-31. http://geodesic.mathdoc.fr/item/TMF_1992_93_1_a1/