New Approach to Multiplicative Stochastic Processes. II: Infinite Number of Time Correlations

A New Approach to Approximate Completion Time Distribution Function of Stochastic Pert Networks

The classical PERT approach uses the path with the largest expected duration as the critical path to estimate the probability of completing a network by a given deadline. However, in general, such a path is not the most critical path (MCP) and does not have the smallest estimate for the probability of completion time. The main idea of this paper is derived from the domination structure between ...

0 Functional integral approach for multiplicative stochastic processes

We present a functional formalism to derive a generating functional for correlation functions of a multiplicative stochastic process represented by a Langevin equation. We deduce a path integral over a set of fermionic and bosonic variables without performing any time discretization. The usual prescriptions to define the Wiener integral appear in our formalism in the definition of Green functio...

Part II CONTINUOUS TIME STOCHASTIC PROCESSES

Contributions to the Theory of Multiplicative Stochastic Processes

The theory of multiplicative stochastic processes is contrasted with the theory of additive stochastic processes. The case of multiplicative factors which are purely random, Gaussian, stochastic processes is treated in detail. In a spirit originally introduced by theoretical work in nuclear magnetic resonance and greatly extended by Kubo, dissipative behavior is demonstrated, on the average, fo...

Empirical Studies of Random Multiplicative Stochastic Processes: Revisit to Lognormals

The statistics involving random multiplicative stochastic processes have been studied empirically. Examples taken here are the duration distribution of disability for aged people, the life span of animals and the population distribution of prefectures in Post-World War II Japan. We found that lognormal distributions show excellent fit with various data for the duration distribution of disabilit...