论文标题
具有乘法噪声的Langevin方程：唯一性，自矛盾和新的解决方案方法通过时间差异方法
Langevin equations with multiplicative noise: uniqueness, self-consistency and new solution methods by a time-discrete approach
论文作者
论文摘要
时间散文方法避免了“集成意义”的假设。新的路径增量（在短时间步长）按照该步骤的顺序完成，而不是当噪声为乘法时的高斯分布；这消除了与Fokker-Planck方程的现有不匹配。通过Markov属性，这些增量可以连续累积，以在任何时候得出解决方案。在一个维度上，通常在一定条件下也表明存在连续时间的极限，并导致路径的“抗ITO”内部填充物。因此，时间步长可以任意减少。路径的数值计算特别准确，因为增量与均值之外的FPE相一致。在上述条件下，FPE采用简单的形式，可以在短时间内明确解决。这允许通过使用Markov属性来计算任何时间的密度函数。
A time-discrete approach avoids the assumption of an 'integration sense'. New path increments (in a short time step) are complete in the order of that step, and not Gaussian distributed when the noise is multiplicative; this eliminates an existing mismatch with the Fokker-Planck equations. By the Markov property these increments can be accumulated in consecutive intervals, to yield the solution for any times. In one dimension, more generally also under a certain condition, it is shown that the limit of continuous time exists and results in the 'anti-Ito' intrgral for the paths; the time step can therefore be diminished arbitrarily. The numerical computation of the paths is particularly accurate, due to increments that agree with the FPE by the mode, in addition to the mean. Under the above condition the FPE takes a simple form and can explicitly be solved for short times; this allows the computation of the density function for any times, by use of the Markov property.
