Java的几何布朗运动

Wiener过程是连续时间随机过程，以纪念Norbert Wiener命名。通常用于用随机成分表示噪音或财务状况。

可以计算几何布朗运动以可视化某些界限（以分位数表示）以暗示绝对范围。为了进行计算，需要以下参数：

µ（mu）：平均百分比
σ（sigma）：方差
t：时间段
v：初始值

常规计算的扩展使用：m：每个时间段的增值（在我的情况下为月度值）中断：分位数中断以计算界限

计算值的代码：

import java.time.LocalDate;
import java.util.*;
import static java.lang.Math.sqrt;
import static java.lang.Math.exp;public class WienerProcess {/*** Run the Wiener process for a given period and initial amount with a monthly value that is added every month. The* code calculates the projection of the value, a set of quantiles and the brownian geometric motion based on a* random walk.** @param mu mean value (annualized)* @param sigma standard deviation (annualized)* @param years projection duration in years* @param initialValue the initial value* @param monthlyValue the value that is added per month* @param breaks quantile breaks* @return a List of double arrays containing the values per month for the given quantile breaks*/public static List<double[]> getProjection(double mu, double sigma, int years, int initialValue,int monthlyValue, double[] breaks) {double periodizedMu = mu / 12;double periodizedSigma = sigma / Math.sqrt(12);int periods = years * 12;List<double[]> result = new ArrayList<double[]>();for (int i = 0; i < periods; i++) {double value = initialValue + (monthlyValue * i);NormalDistribution normalDistribution = new NormalDistribution(periodizedMu * (i + 1),periodizedSigma * sqrt(i + 1));double bounds[] = new double[breaks.length];for (int j = 0; j < breaks.length; j++) {double normInv = normalDistribution.inverseCumulativeProbability(breaks[j]);bounds[j] = value * exp(normInv);}result.add(bounds);}return result;}
}

应用值：