All Questions
Tagged with simulation stochastic-processes
46
questions
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37
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How to guess a random walk to achieve max sample correlation?
Define this 1-D discrete random walk start from 0: roll a die (the die may or may not be fair, the fixed probability of each face is unknown to the observer/guessor)...
- 53
1
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30
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Extended Hidden Markov Models (HMM) parameter estimation
For simpler HMMs, we can use algorithms like Viterbi training (not decoding) or Baum Welch to estimate the parameters that best describe the observed data.
How do we do the same when using a more ...
- 63
1
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0
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212
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Monte Carlo simulation vs. Discrete event simulation
I'm trying to understand the difference between a Monte Carlo simulation vs. a Discrete event simulation. I learned from googling( for eg.: https://bookdown.org/manuele_leonelli/SimBook/types-of-...
- 357
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114
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Simulating Nonhomogeneous Poisson Process - Conditional distribution of arrival times
For a Poisson process having rate $\lambda$. Given the number of events by time $T$ the set of event times are iid Uniform $(0,T)$ random variables. Suppose that each event are independently counted ...
- 359
3
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63
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Gillespie's Algorithm's Connection to Kolmogorov's Forward Equations
I've been learning Gillespie's algorithm to simulate continuous time Markov chains. I understand how the algorithm is derived from the reaction probability density function
$P(\tau, \mu)$ = ...
- 31
4
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2
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151
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Simulating a process
Let $W$ be a random variable valued in $L^2[0,1]$ (an infinite dimensional function space). Take $W=\{W(t), t\in[0,1]\}$ on $[0,1]$.
$$W(t)=\sum_{i=1}^\infty e_i(t) N_i, \quad \forall t\in [0,1]$$
...
- 1,097
1
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1
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138
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What's the transition probability according to this PDE?
I'm trying to figure out how I can simulate markov chains based on an ODE:
dN/dt = alpha N (1 - N / K) - beta N
Thus N denotes ...
- 123
1
vote
1
answer
233
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How to simulate non-gaussian stochastic paths
(Edited to be clearer)
I am trying to replicate simulating Geometric Brownian Motion (GBM) but instead of the stochastic increment following a normal distribution, I would like it to follow a ...
- 13
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161
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Simulating paths of stochastic process from density
I need yout help! I have a stochastic process $X_t$ and I know its density function $f(x,t)$, which is defined for $x>t$.
I'm looking for a code in R that simulates the paths of the process, so I ...
- 1
30
votes
5
answers
3k
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What are examples of statistical experiments that allow the calculation of the golden ratio?
There are some very simple experiences that can be done by a kid at home, whose result allows one to statistically approach famous numbers such as $\pi$ or $e$.
An example where $\pi$ shows up is ...
- 1,733
1
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1
answer
74
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Why does my simulation of nearest neighbors as circle origins provide different non-contact probability compared to theoretical?
I am simulating spatially distributed points in $\mathbb{R}^2$ with intensity $\lambda$ (units 1/area), which act as circle origins with radii being a random variable $R_k$. Given the distance to the $...
- 11
2
votes
1
answer
423
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Simulation of compound Poisson Process with Lognormal jumps?
So I have the next problem:
In order to simulate the ruin of a risk process I need, of course, to simulate the risk process itself but in this case this process has some characteristics that make it ...
1
vote
1
answer
630
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Simulating exponential Vasicek/Ornstein-Uhlenbeck
I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from Schwartz 1997 p. 926 Equation (1). I am using the closed form solution from Vega 2018 p. 5 Equation ...
- 11
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votes
1
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534
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Geometric Brownian motion with target skewness and kurtosis
The Cholesky inversion method can be adopted to set a target correlation matrix when artificially generating a multivariate geometric Brownian motion dataset
Can the moments of a univariate GBM be ...
- 4,025
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109
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Gaussian processes and generating functions from a distribution?
Some points in Rasmussen book on Gaussian processes are confusing, when he says that the first step in some GP regression is
In Figure1.1(a) we show a number of sample functions drawn at random
...
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