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@IlievskiV
Created June 5, 2020 21:22
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Demonstration of the reflection principle of the Brownian Motion
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Reflection Principle for Brownian Motion"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# import libraries\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.animation as animation\n",
"\n",
"# ignore warnings\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n",
"# set the seed\n",
"np.random.seed(42)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulate Brownian Motion"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def brownian_motion(N, T, h, seed=42):\n",
" \"\"\"Simulates a Brownian motion.\n",
" \n",
" :param int N : number of discrete steps\n",
" :param int T: number of continuous time steps\n",
" :param float h: variance of the increments\n",
" :param int seed: initial seed of the random generator\n",
" :returns tuplpe: the brownian motion and its increments\n",
" \"\"\"\n",
" # set the seed\n",
" np.random.seed(seed)\n",
" # the normalizing constant\n",
" dt = 1. * T/N\n",
" # the epsilon values\n",
" random_increments = np.random.normal(0.0, 1.0 * h, N)*np.sqrt(dt)\n",
" # calculate the brownian motion\n",
" brownian_motion = np.cumsum(random_increments)\n",
" # insert the initial condition\n",
" brownian_motion = np.insert(brownian_motion, 0, 0.0)\n",
" \n",
" return brownian_motion, random_increments"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Generate the two processes"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"N = 10000 # number of discret points\n",
"T = 10 # number of time units\n",
"h = 2.75 # variance of the incremennts\n",
"seed = 1234 # the seed to use\n",
"dt = 1.0 * T/N # total number of time steps\n",
"\n",
"W, _ = brownian_motion(N, T, h, seed) # standard Brownian Motion\n",
"min_W = np.min(W) # min of W\n",
"\n",
"t = np.linspace(0.0, N*dt, N+1)\n",
"\n",
"a = 7.5 # the target value\n",
"a_idx = np.argwhere(W > a)[0][0] # index of the target value\n",
"line_a = [a]*(N+1) # the line for the threshold value\n",
"\n",
"# generate the reflective process\n",
"W_star = [0]*(N+1)\n",
"W_star[:a_idx+1] = W[:a_idx+1]\n",
"W_star[a_idx+1:] = 2*a - W[a_idx+1:]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Make the Animation"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1080x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(15, 7))\n",
"ax = plt.axes(xlim=(0, T), ylim=(round(np.min(W_star)), round(np.max(W))))\n",
"\n",
"# formatting options\n",
"ax.set_title('Reflection Principle for Brownniann Motion', fontsize=24)\n",
"ax.set_xlabel('Time', fontsize=22)\n",
"ax.set_ylabel('Value', fontsize=22)\n",
"ax.set_xticks(np.linspace(0, T, 2*T + 1))\n",
"ax.tick_params(labelsize=18)\n",
"ax.grid(True, which='major', linestyle='--', color='black', alpha=0.6)\n",
"\n",
"threshold_line, = ax.plot(t, line_a, linestyle='-.', color='black', label='$T_{a} = 7.5$')\n",
"threshold_point = ax.scatter(t[a_idx], a, s=100, c='k')\n",
"\n",
"w_line, = ax.step([], [], where='mid', lw=1, color='#0492c2') # line for the Brownian Motion\n",
"w_star_line, = ax.step([], [], where='mid', lw=1, color='#ff4500') # line for the reflected\n",
"\n",
"ax.legend(loc=2)\n",
"\n",
"# animation options\n",
"frames = 400\n",
"factor = N // frames\n",
"\n",
"offset = (a_idx + 1) % factor\n",
"remainder = factor - offset\n",
"\n",
"def animate(i):\n",
" if (i + 1)*factor + offset < a_idx + 1:\n",
" upper_bound = (i + 1)*factor + offset\n",
" else:\n",
" upper_bound = (i + 1)*factor\n",
" w_star_line.set_data(t[(a_idx + 1):upper_bound], W_star[(a_idx + 1):upper_bound])\n",
" \n",
" w_line.set_data(t[:upper_bound], W[:upper_bound])\n",
" plt.gcf().text(0.15, 0.05, '@VladOsaurus', fontsize=18)\n",
" \n",
" return w_line, w_star_line,\n",
"\n",
"# call the animator\t \n",
"anim = animation.FuncAnimation(fig, animate, frames=frames, interval=25, blit=True)\n",
"# save the animation as mp4 video file \n",
"anim.save('reflection_principle_bm.gif',writer='imagemagick') "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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