Euler–Maruyama method
E31546
The Euler–Maruyama method is a basic time-stepping scheme for numerically approximating solutions to stochastic differential equations, widely used in simulations of systems with noise such as Langevin dynamics.
Aliases (1)
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
method for stochastic differential equations
→
numerical method → time-stepping scheme → |
| appliesTo |
Itô stochastic differential equations
→
SDEs driven by Brownian motion → |
| basedOn |
Euler method
→
|
| category |
stochastic numerical analysis
→
|
| comparedTo |
Milstein method
→
higher-order stochastic Runge–Kutta methods → |
| field |
applied mathematics
→
|
| generalizes |
Euler method to stochastic differential equations
→
|
| hasLimitation |
low strong order of convergence
→
may be unstable for stiff SDEs → may require small time steps for accuracy → |
| hasOrderOfConvergence |
strong order 0.5
→
weak order 1 → |
| hasProperty |
conditionally stable
→
low computational cost per step → simple to implement → |
| introducedBy |
Gisiro Maruyama
→
|
| introducedIn |
1950s
→
|
| isDiscretizationOf |
Itô integral
→
|
| isExplicit |
true
→
|
| isFirstOrderMethod |
true
→
|
| isOneStepMethod |
true
→
|
| isSpecialCaseOf |
stochastic Runge–Kutta method
→
|
| namedAfter |
Gisiro Maruyama
→
Leonhard Euler → |
| relatedTo |
Langevin equation
→
Ornstein–Uhlenbeck process → geometric Brownian motion → |
| requires |
time discretization
→
time step size selection → |
| usedFor |
Langevin dynamics simulations
→
numerical approximation of stochastic differential equations → simulation of stochastic processes → simulation of systems with noise → |
| usedIn |
Monte Carlo simulations of SDEs
→
biology → chemistry → climate modeling → computational finance → engineering → neuroscience → physics → quantitative risk management → |
| uses |
Brownian motion increments
→
Gaussian random variables → |
Referenced by (2)
| Subject (surface form when different) | Predicate |
|---|---|
|
Euler–Maruyama method
("stochastic Runge–Kutta method")
→
|
isSpecialCaseOf |
|
Langevin dynamics
→
|
numericalSchemes |