Moreno Miguel V, Barci Daniel G, Arenas Zochil González
Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Rio de Janeiro, RJ, Brazil.
Departamento de Matemática Aplicada, IME, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013 Rio de Janeiro, RJ, Brazil.
Phys Rev E. 2019 Mar;99(3-1):032125. doi: 10.1103/PhysRevE.99.032125.
We address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach. We show the equivalence between the conditional probability and the propagator of a quantum particle with variable mass. Introducing a time reparametrization, we are able to transform the problem of multiplicative noise fluctuations into an equivalent additive one. We illustrate the method by showing the explicit analytic computation of the conditional probability of a harmonic oscillator in a nonlinear multiplicative environment.
我们使用路径积分方法来处理乘性噪声随机微分方程中的转移概率计算问题。我们展示了条件概率与具有可变质量的量子粒子的传播子之间的等价性。通过引入时间重新参数化，我们能够将乘性噪声涨落问题转化为一个等效的加性噪声问题。我们通过展示在非线性乘性环境中一个谐振子条件概率的显式解析计算来说明该方法。
