# Questions tagged [brownian]

Brownian motion is the random motion of particles (eg atoms) that make up a gas. The math used to model Brownian motion is sometimes used in statistics to describe stochastic processes over time.

89 questions
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### Discretization simulation of a Wiener Process

I got some problems with this homework which I have totally no idea, never got into this field before and I really need some help. First, we have a wiener process like Which means the probability of ...
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### Option Pricing Macro/Addin in Excel or R Function to Capture Arbitrary Payoff Formula on Underlying Prices

I am looking for an option pricer in Excel or R package that can price a payoff that could be some formula on the underlying prices and interest rate. This means the option payoff could depend on ...
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### LSTM Fitting Random Walk

I've got a question about an LSTM neural net fitting a random walk. I've made the LSTM [network shape: 1, 50, 100, 200, 50, 1] and out of interest made a completely random walk (by using a normal ...
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### Why does the Hurst package apply a finite-differencing step before doing rescaled range calculations?

When I look at the code for the compute_Hc function in the Hurst package for Python, there is an initial finite differencing step. Everything else after that agrees ...
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### Simulating a stochastic integral

I am trying to solve exercise 3.9.10 on p. 66 of Ubbo F. Wiersema's "Brownian Motion Calculus" (John Wiley & Sons, 2008), which asks to simulate the stochastic integral $$\int_0^1 B(t)\ dB(t)$$ ...
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### Conditional Expectation Brownian Motion

So this is an exam question I had recently and I honestly had no idea on how to solve it. Let W(t) be a Brownian Motion stochastic process at time t with drift p and variance v^2 Let s exist such ...
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### Modelling startups' funding journey with Brownian Motion

I am trying to implement a "light" version of a paper (Hunter, Saini & Zaman 2017), in which the authors build a model capable of predicting the probability that a startup will exit (either by ...
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### Distribution of Conditional Brownian Motion

Let $\ X(t),t \ge 0$ be a Brownian motion process. That is, $\ X(t)$ is a process with independent increments such that: $$\ X(t) - X(s) \sim N(0,t-s), 0\le s \lt t$$ and $\ X(0)= 0$. ...
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### Generating fractional Brownian motion in R [closed]

I was trying to generate fractional Brownian motion in R using fbm of the package somebm. However, in this package, I can not ...
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### What is the distribution of the peak time of the first hitting time process

I need to find the distribution of the random variable $T_{peak}$ where $T_{peak}$ represents the peak time of the first hitting time process. Detailed Explanation of the System: There are $N^{Tx}$ ...
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### Brownian Motion proof: difference converging to 0 almost surely

I am reading a proof where it is assumed that $$\lim_{n \to \infty} \sup_{0<s\leq s_0}\left| \frac{t_n(s)}{s}-1 \right|=0 , \hspace{30mm} (1)$$ where $t_n(.)$ is some sequence of functions. ...
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### How to transform a unit root process to a stationary process?

If a time series has a unit root, that can be modeled as discretized geometric Brownian motion, then are there any ways to reduce the series to $\sim I(0)$? subject to the fact that no other time ...
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### Power Spectral Density of Random Walk

The Brownian motion has a power spectral density (PSD) dependency on frequency like $\frac{1}{f^2}$. As far as I understand, power spectral density is defined only for wide sense stationary processes ...
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### Is standard Brownian motion (AKA a Wiener process) weakly or strictly stationary?

Question Let $B(t)$ be a standard Brownian motion (AKA a Wiener process). Is $B(t)$ weakly or strictly stationary, particularly as defined here? My Thoughts We know, by definition, that its ...
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### How to solve / fit a geometric brownian motion process in Python?

For example, the below code simulates Geometric Brownian Motion (GBM) process, which satisfies the following stochastic differential equation: The code is a condensed version of the code in this ...