Mapping multiplicative to additive noise

Abstract

The Langevin formulation of a number of well-known stochastic processes involves multiplicative noise. In this work we present a systematic mapping of a process with multiplicative noise to a related process with additive noise, which may often be easier to analyse. The mapping is easily understood in the example of the branching process. In a second example we study the random neighbour (or infinite range) contact process which is mapped to an Ornstein-Uhlenbeck process with absorbing wall. The present work might shed some light on absorbing state phase transitions in general, such as the role of conditional expectation values and finite size scaling, and elucidate the meaning of the noise amplitude. While we focus on the physical interpretation of the mapping, we also provide a mathematical derivation.

22 pages, 4 figures, IOP style

References in corpus (3)

• Prediction and predictability of global epidemics: the role of the airline transportation network
• Closed-form likelihood expansions for multivariate diffusions
• Equivalence of conditional and external field ensembles in absorbing state phase transitions

Cited by in corpus (8)

• Sample and population exponents of generalized Taylor's law
• Run-and-tumble motion: field theory and entropy production
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
• Time-series thresholding and the definition of avalanche size
• Multiplicative noise and heavy tails in stochastic optimization
• The perils of thresholding
• Conditional probabilities in multiplicative noise processes
• Method of Higher-Order Operators for Quantum Optomechanics