乘性噪声到加性噪声的映射
Mapping multiplicative to additive noise
摘要：
一些著名的随机过程的朗之万公式涉及乘性噪声。在这项工作中，我们提出了一个系统的映射与乘性噪声的相关过程与加性噪声，这可能往往是更容易分析。在分支过程的例子中，映射很容易理解。在第二个例子中，我们研究随机邻居（或无限范围）接触过程映射到一个Ornstein-Uhlenbeck过程的吸收壁。目前的工作可能会揭示一些光的吸收状态相变一般，如条件期望值和有限尺寸标度的作用，并阐明了噪声幅度的含义。虽然我们专注于映射的物理解释，我们也提供了一个数学推导。
英文摘要：
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.
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