StochasticProcesses/simpleRandomWalk.R at master · EthutengDev/StochasticProcesses · GitHub

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rm(list = ls())
#simple random walk simulation
simpleRandomWalk <- function(initialState, n, theta){
  yt = numeric(n);
  yt[1] = initialState; #initial state

  if(theta > 1 || theta < 0){ #probabilities are between 0 and 1

    return('Invalid value for theta')

  } else {

    #stepSize := et = 1 or -1 with P(stepSize = 1) = theta, and P(stepSize = -1) = 1-theta
    stepSize = sample(c(1, -1), size = n, prob = c(theta, 1-theta), replace = TRUE);

    for(i in 2:length(yt)){

      yt[i] = yt[i-1] + stepSize[i];
    }
    return(yt);

  }

}

expectedValueSRW <- function(initialState, n, theta){

  if(theta > 1 || theta < 0){
    return('Invalid value for theta')
  } else {
    #expected value of Xn given xo in a simple random walk
    expectedValueXn = initialState + abs(n)*(2*theta - 1);
    return(expectedValueXn);
  }

}

expectedValueVectorSRW <- function(initialState, n, thetas){
  #initialise an empty expected values vector that's going to
  #store a collection of expected values for different values of
  #theta
  expectedValueVector = numeric();
  for (i in 1:length(thetas)) {
    expectedValueVector[i] = expectedValueSRW(initialState, n, thetas[i]);
  }

  return(expectedValueVector);

}

simExpectedValueSRW <- function(initialState, n, theta){
  simulatedExpectedValue = numeric();
  for (i in 1:n) {
    simulatedExpectedValue[i] = mean(simpleRandomWalk(initialState, n, theta));

  }

  #return a simulated Expected value of Xn given Xo
  return(mean(simulatedExpectedValue));
}

varianceSRW <- function(n, theta){

  if(theta > 1 || theta < 0){
    return('Invalid value for theta')
  } else {
    #variance of Xn given xo in a simple random walk
    varianceXn = 4*n*theta*(1 - theta);
    return(varianceXn);
  }

}


varianceVectorSRW <- function(n, thetas){
  #initialise an empty variance vector that's going to
  #store a collection of variances for different values of
  #theta
  varianceVector = numeric();
  for(i in 1:length(thetas)){
    varianceVector[i] = varianceSRW(n, thetas[i]);
  }

  return(varianceVector);
}