New Approach to Multiplicative Stochastic Processes. I: Long-Time Statistics and Fluctuation-Spectrum Theory

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...

Fluctuation Theory and Stochastic Games for Spectrally Negative Lévy Processes

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...

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 ...

Stochastic multiplicative processes with reset events.

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is...