我想模拟一个非线性随机微分方程
在哪里和是一维标准布朗运动。我怎样才能通过 MATLAB 做到这一点？
类似方程的良好模拟文件可能会有所帮助。
随机微分方程（SDE）数值解的例子？
计算科学
数值分析
随机
2021-12-23 13:23:05
2个回答
查看Des Higham的这篇论文和SDETools MATLAB 工具箱。
% EM Euler-Maruyama method on linear SDE
%
% SDE is dX = lambda*X dt + mu*X dW, X(0) = Xzero,
% where lambda = 2, mu = 1 and Xzero = 1.
%
% Discretized Brownian path over [0,1] has dt = 2^(-8).
% Euler-Maruyama uses timestep R*dt.
state=randn(100)
lambda = 2;
mu = 1;
Xzero = 1; % problem parameters
T = 1;
N = 2^8;
dt = 1/N;
dW = sqrt(dt)*randn(1,N); % Brownian increments
W = cumsum(dW); % discretized Brownian path
Xtrue = Xzero*exp((lambda-0.5*mu^2)*([dt:dt:T])+mu*W);
plot([0:dt:T],[Xzero,Xtrue]), hold on
R = 4;
Dt = R*dt;
L = N/R; % L EM steps of size Dt = R*dt
Xem = zeros(1,L); % preallocate for efficiency
Xtemp = Xzero;
for j = 1:L
Winc = sum(dW(R*(j-1)+1:R*j));
Xtemp = Xtemp + Dt*lambda*Xtemp + mu*Xtemp*Winc;
Xem(j) = Xtemp;
end
plot([0:Dt:T],[Xzero,Xem]), hold off
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