A functional Stieltjes measure and generalized diffusion processes

H. Dekker

Physica A: Statistical Mechanics and its Applications, 1977, vol. 87, issue 2, 419-425

Abstract: The sum over paths for a generalized Wiener diffusion process has been presented in a previous paper on the basis of the concept of time-local gaussian processes. This well-defined functional sum leads to a functional integral for the probability of passing from an initial state to some final state of the system. A mathematical ambiguity remained in the freedom to choose the diffusion function in the measure anywhere between the so-called prepoint for each infinitesimal transition. In the present paper we will demonstrate, for the generalized diffusion process, how a logical extension of functional integration in the sense of Stieltjes quite naturally leads to an unambiguous formulation which has the special and interesting property of being form-invariant under nonlinear transformations according to the rules of ordinary differential calculus.

Date: 1977
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:87:y:1977:i:2:p:419-425

DOI: 10.1016/0378-4371(77)90028-0

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