Stochastic Differential Equations
Simulate SDEs with Euler-Maruyama — geometric Brownian motion, Ornstein-Uhlenbeck, and more.
Sample Paths
Run / Restart
Pause
Clear
SDE Model
Process:
GBM
O-U
CIR
BM
Custom
μ (drift):
0.10
σ (volatility):
0.30
θ (mean-rev speed):
1.00
μ̄ (long-run mean):
1.00
Number of paths:
10
Time horizon T:
5.0
dX = μX dt + σX dW (GBM)
Euler-Maruyama: X_{t+h}=X_t+f(X_t)h+g(X_t)√h·N(0,1)
Time:
0.00
Mean X(t):
—
Std X(t):
—
Paths running:
0
GBM = Geometric Brownian Motion (Black-Scholes). O-U = Ornstein-Uhlenbeck (mean reverting). CIR = Cox-Ingersoll-Ross (interest rates, stays positive). Each step uses Euler-Maruyama discretization with step size h=dt.