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@mschauer
Last active October 4, 2018 04:08
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Assortment of stochastic processes with Bridge.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Assortment of stochastic processes with Bridge"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"using Plots\n",
"using Bridge"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [],
"source": [
"# define time grid\n",
"dt = 1/1000\n",
"t = 0:dt:1;"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Wiener process [(Wikipedia)](https://en.wikipedia.org/wiki/Wiener_process)\n",
"Continuous process with independent Gaussian increments, integral of a white noise Gaussian process."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sample(t, Wiener()), fmt = :png)\n",
"scatter!([0], [0], legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Gamma process [(Wikipedia)](https://en.wikipedia.org/wiki/Gamma_process)\n",
"An increasing random process with independent Gamma distributed increments (a Levy process)."
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sample(t, GammaProcess(10.0, 1.0)), fmt = :png)\n",
"scatter!([0], [0], legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Brownian Bridge [(Wikipedia)](https://en.wikipedia.org/wiki/Brownian_bridge)\n",
"A Wiener process conditional on hitting 0 at time 1."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sample(t, WienerBridge(1.0, 0.0)), fmt = :png)\n",
"scatter!([0,1], [0,0], legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Brownian excursion [(Wikipedia)](https://en.wikipedia.org/wiki/Brownian_excursion)\n",
"A Brownian bridge conditioned to stay positive. Also a 3 dimensional Bessel process conditional on hitting 0 at time 1. "
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(sample(eps(), t, Bridge.Bessel3Bridge(1.0, 0.0, 1.0)),fmt = :png)\n",
"scatter!([0,1], [eps(),0], legend=false)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Inhomogenous Poisson process [(Wikipedia)](https://en.wikipedia.org/wiki/Poisson_process)\n",
"A counting process representing the total number of occurrences or events happening up to time \n",
"$t$ with time dependent rate function $\\lambda(t) > 0$ sampled using the thinning-algorithm."
]
},
{
"cell_type": "code",
"execution_count": 96,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 96,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"λ(t) = 100 + 100sin(t)\n",
"λmax = 200.0\n",
"times = sample(ThinningAlg(λmax), 1, InhomogPoisson(λ))\n",
"plot(times, 1:length(times), legend=false, fmt=:png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### FitzHugh–Nagumo model [(Wikipedia)](https://en.wikipedia.org/wiki/FitzHugh–Nagumo_model)\n",
"\n",
"The stochastic FitzHugh–Nagumo model is a 2D stochastic differential equation describing a prototype of an excitable system (e.g., a neuron)."
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"
},
"execution_count": 93,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using StaticArrays\n",
"using Bridge.Models\n",
"\n",
"R2 = SVector{2,Float64}\n",
"W = sample( 0:dt:20, Wiener())\n",
"struct FitzHughNagumo <: ContinuousTimeProcess{R2}\n",
" ϵ::Float64\n",
" s::Float64\n",
" γ::Float64\n",
" β::Float64\n",
" σ::Float64\n",
"end\n",
"\n",
"Bridge.b(t, x, P::FitzHughNagumo) = R2((x[1]-x[2]-x[1]^3+P.s)/P.ϵ, P.γ*x[1]-x[2] +P.β)\n",
"Bridge.σ(t, x, P::FitzHughNagumo) = R2(0.0, P.σ)\n",
"\n",
"P = FitzHughNagumo(0.1, 0.0, 1.5, 0.8, 0.3) # Ditlevsen-Samson\n",
"X = solve(Euler(), zero(R2), W, P)\n",
"plot(X.tt, first.(X.yy), fmt=:png, label=\"Action potential\")\n",
"plot!(X.tt, last.(X.yy), label=\"Latent component\")\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.7.0",
"language": "julia",
"name": "julia-0.7"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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