Path reparametrization in a path integral on a finite-dimensional manifold

The methods of the theory of random processes are used to investigate the general case of reparametrization in a path integral defined on an n-dimensional manifold; the integral represents the solution of the Schroedinger equation in imaginary time. The main result of the paper is the derivation of the formula proposed earlier or the Jacobian of the reparametrization in the path integral. We first define the path integral, then study the properties of the integral associated with reparametrization, and finally, on the basis of these properties, we formulate a rule for reparametrization in the symbolic expression of the path integral