All Questions
5
questions
1
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101
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Use Bayes method to solve ODE system with random noise
For ODE system $\frac{du}{dt} = \beta u$, $t>0$, $u(0)=1$, where $\beta$ is unknown. But the solution to the system at t=1 up to some noise is known: $h :=u(1) + \zeta$, where $\zeta$ is a random ...
- 113
0
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1
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312
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Write down the backward equations for $P_{12}$ and $P_{21}$ and use the symmetry of Q to solve these equations.
Hint: Whenever confronted with an ordinary differential equation of the form x′(t) = ax(t)+b(t), it might be beneficial to consider the function y(t) = $e^{−at}x(t)$.
$$Q = \left[ \begin{matrix}
...
- 253
0
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0
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117
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Understanding the stochastic SIR model
I am learning about what it means for a model to be Stochastic. To do this, I am examining the stochastic SIR model found here: https://en.wikipedia.org/wiki/Gillespie_algorithm (scroll down to the ...
0
votes
2
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351
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Is jump intensity inaccurate in describing random process?
In https://en.wikipedia.org/wiki/It%C3%B4's_lemma
Under the section of Poisson jump processes, it is said that
We may also define functions on discontinuous stochastic processes.
Let h be the jump ...
- 948
1
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1
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2k
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Finding mean and variance of stochastic process
If I'm given a Stochastic Process Xt that satisfies a stochastic diff. equation, let's say fXt,
what is the formula to find the mean and variance of Xt?
I think it's:
$mean = dE(X_t) = dX_0e^t$
$...
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