Questions tagged [simulation]

A vast area which includes generating results from computer models.

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Conditional Variance Implementation, Integral approximation with Monte Carlo

as part of my master's thesis, I have to implement the following conditional variance \begin{align*} \mathbb{V}ar[\hat{v}|\hat{y}] &= \mathbb{E}\left[\hat{v}^{2} \mid \hat{y}\right] - \mathbb{E}\...
20 views

Real Life Example for Jackson Network

I have this jackson network with the provided arrival flow rates and service rates, can anyone provide me a real life example for this network having as unit of measure job/sec or job/min for the ...
14 views

Simulating from differential equation inside Point Process

I've been reading Stochastic Epidemic Models with Inference by Britton and Pardoux where I found the following notation for the Markovian SIR model: I was looking for references/guidance on how could ...
21 views

Searching sample distribution with given parameteres

I have a very simple question, but it is hard, at least to me, for giving a solution. Given values of mean, variance and median, can you find a method to generate a random sample with these parameters?...
12 views

How do I calculate this Probability in two Constraints (Cell Population Simulation)

I am simulating Cell Populations of Stem Cells and I've come across this equation in an article: $P_{SC} = P_{SC} (N_{SC}, N_{EP} , N_{LP} , N_{MC} ) \in [P_{min,SC} , P_{max,SC }]$ Symbol explanation:...
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Simulating from some polynomial distributions

Let $f:\mathcal{R}^+\to \mathcal{R}^+$ a continuous distribution of the type $$f(x|a_0,a_1,\cdots,a_n)=\frac{1}{k}(a_0+\sum_{i=1} a_i x^i),$$ where $a_0,a_1,\cdots,a_n$ are given parameters and $k$ ...
20 views

Multivariate control variate technique

In the control variate technique, one tries to improve convergence of the expected value of a random variable $X$, estimated from simulating a range of $n$ Monte Carlo simulations. This is done by ...
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Calculate the covariance matrix for three random variables

I have the task: The random values $X$, $Y$ and $Z$ are related by the ratio $2X -3Y + Z = 0$. Moreover, $EX = EY = EZ = 0$, $DX = 2, DY = 1, DZ = 5$. Calculate the covariance matrix $\Lambda$ of ...
43 views

Absorption Times of Markov Chains in Continuous State-Space

I have the following question about the Absorption Times of Markov Chains in Continuous State-Space. I was reading the following article on Absorption Times of Markov Chains (https://en.wikipedia.org/...
42 views

Brownian Motion with initial value different than 0, Expected value?

Im trying to simulate brownian motion and brownian motion with drift and i know they have properties like: $B(0) = 0 \$ almost surely $B(t) \ \text{has distribution } N(0,t \sigma ^2)$ But what ...
144 views

Simulating Coin Flips vs Probability of Coin Flips

Is there a standard formula for calculating the maximum, minimum and average number of times you need to flip a coin before observing a desired sequence? Suppose you have a coin that has a 95% chance ...
31 views

Simulate a Markov chain subject to known values at some time steps

I am working with a natural process (occurrence of rock types along a vertical well) that can be modeled as a Markov chain. The (finite) state space and the transition matrix (or transition rate ...
49 views

Simulating a random process with correlation structure $e^{-|t-s|}$
Consider a random process $X_t$ such that $$dX_t\sim N(0,dt)$$ and $$\operatorname{corr}(dX_t,dX_s)=e^{-k|t-s|}.$$ This question is probably trivial but how can I simulate the path path of $X_t$? Any ...
How to simulate $E[X | \mathcal F_t]$ when there is no Markovianity?
Let $(\mathcal F_t)$ be a filtration and $X$ a random variable such that $E[X | \mathcal F_t] \neq X$ and $E[X | \mathcal F_t] \neq E[X]$ for all $t\in [a,b]$. We consider the conditional expectation \$...