AIUQ (version 0.5.3)

anisotropic_fbm_ou_particle_intensity: Simulate 2D particle trajectory follows anisotropic fBM plus OU

Description

Simulate 2D particle trajectory follows anisotropic fraction Brownian Motion(fBM) plus a Ornstein–Uhlenbeck(OU) process for M particles, with different step sizes in x, y-directions.

Usage

anisotropic_fbm_ou_particle_intensity(
  pos0,
  M,
  len_t,
  sigma_fbm,
  sigma_ou,
  H,
  rho
)

Value

Position matrix with dimension M\(\times\)len_t

by 2 for particle trajectory. The first M rows being the initial position pos0.

Arguments

pos0

initial position for M particles, matrix with dimension M by 2

M

number of particles

len_t

number of time steps

sigma_fbm

distance moved per time step in fractional Brownian Motion in x, y-directions, a vector of length 2

sigma_ou

distance moved per time step in Ornstein–Uhlenbeck process in x, y-directions, a vector of length 2

H

Hurst parameter of fractional Brownian Motion in x, y-directions, a vector of length 2 with values between 0 and 1

rho

correlation between successive step and previous step in OU process in x, y-directions, a vector of length 2 with values between 0 and 1

Author

tools:::Rd_package_author("AIUQ")

Examples

library(AIUQ)
M = 10
len_t = 50
sigma_fbm = c(2,1)
H = c(0.3,0.4)
sigma_ou = c(2,2.5)
rho = c(0.95,0.9)
pos0 = matrix(100/8+0.75*100*runif(M*2),nrow=M,ncol=2)

pos = anisotropic_fbm_ou_particle_intensity(pos0=pos0, M=M, len_t=len_t,
  sigma_fbm=sigma_fbm, sigma_ou=sigma_ou, H=H, rho=rho)