rw.sim <- function( k, p, theta.start, n.sim, seed ) {

  set.seed( seed )  

  theta <- rep( 0, n.sim + 1 )

  theta[ 1 ] <- theta.start

  for ( i in 1:n.sim ) {

    theta[ i + 1 ] <- move( k, p, theta[ i ] )

  }

  return( table( theta ) )

}

move <- function( k, p, theta ) {

  repeat {

    increment <- sample( x = c( -1, 0, 1 ), size = 1, prob = p )

    theta.next <- theta + increment

    if ( abs( theta.next ) <= k ) {

      return( theta.next )

      break

    }

  }

}

p <- c( 1, 1, 1 ) / 3

k <- 5

theta.start <- 0

seed <- c( 6425451, 9626954 )

rw.sim( k, p, theta.start, 10, seed )

rw.sim( k, p, theta.start, 100, seed )

rw.sim( k, p, theta.start, 1000, seed )

rw.sim( k, p, theta.start, 10000, seed )

rw.sim( k, p, theta.start, 100000, seed )

rw.sim( k, p, theta.start, 1000000, seed )

rw.sim( k, p, 5, 100000, seed )

p <- c( 0.2, 0.3, 0.5 )

rw.sim( k, p, 0, 10, seed )

rw.sim( k, p, 0, 100, seed )

rw.sim( k, p, 0, 1000, seed )

rw.sim( k, p, 0, 10000, seed )

rw.sim( k, p, 0, 1000000, seed )