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A functional Stieltjes measure and generalized diffusion processes

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  • Dekker, H.

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.

Suggested Citation

  • Dekker, H., 1977. "A functional Stieltjes measure and generalized diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 87(2), pages 419-425.
    • Handle: RePEc:eee:phsmap:v:87:y:1977:i:2:p:419-425
    DOI: 10.1016/0378-4371(77)90028-0
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