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Simulate 1-3D Markovian Stochastic Differential Equations

Source: R/simulation.R
sim_SDE.Rd

A wrapper to the simulation utilities provided by the Sim.DiffProc package. You may skip this step and write your own simulation function for more customized simulation.

Usage

sim_SDE(
  N = 1000,
  M = 1,
  x0,
  t0 = 0,
  T = 1,
  Dt = rlang::missing_arg(),
  drift,
  diffusion,
  corr = NULL,
  alpha = 0.5,
  mu = 0.5,
  type = "ito",
  method = "euler",
  keep_full = TRUE
)

Arguments

N

The number of time steps.

M

The number of simulations.

x0

The initial values of the SDE. The number of values determine the dimension of the SDE.

t0

initial time.

T

terminal time.

Dt

time step. If missing, default will be (T - t0) / N.

drift

An expression of the drift function. The number of expressions determine the dimension of the SDE. Should be the function of t, x, y and z (y and z are only included for 2D or 3D cases).

diffusion

An expression of the diffusion function. The number of expressions determine the dimension of the SDE. Should be the function of t, x, y and z (y and z are only included for 2D or 3D cases).

corr

The correlations between the Brownian motions. Only used for 2D or 3D cases. Must be a real symmetric positive-definite matrix of size 2x2 or 3x3. If NULL, the default is the identity matrix.

alpha, mu

weight of the predictor-corrector scheme; the default alpha = 0.5 and mu = 0.5.

type

if type="ito" simulation sde of Itô type, else type="str" simulation sde of Stratonovich type; the default type="ito".

method

numerical methods of simulation, the default method = "euler".

keep_full

Whether to keep the full snssde1d/snssde2d/snssde3d object. If TRUE, the full object will be returned. If FALSE, only the simulated values will be returned as a matrix or a list of matrices (when M >= 2).

Value

Depending on the value of keep_full, the output will be a list of snssde1d, snssde2d or snssde3d objects, or a matrix or a list of matrices of the simulated values.

Examples

# From the Sim.DiffProc package

set.seed(1234, kind = "L'Ecuyer-CMRG")
mu <- 4
sigma <- 0.1
fx <- expression(y, (mu * (1 - x^2) * y - x))
gx <- expression(0, 2 * sigma)
mod2d <- sim_SDE(drift = fx, diffusion = gx, N = 1000,
Dt = 0.01, x0 = c(0, 0), type = "str", method = "rk1",
M = 2, keep_full = FALSE)
#> Error in eval(drifty): object 'mu' not found

print(as.mcmc.list(mod2d))
#> Error: object 'mod2d' not found