Questions tagged [laplace-method]

Laplace's method is a way of approximating integrals and related quantities, like expectations, see https://en.wikipedia.org/wiki/Laplace%27s_method

182 questions
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laplace transform two forms

$$L[f'''(t)]=\int e^{-st}f'(t)dt=L[f'(t)]$$ im not sure if this is how it works. please advice
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How to approximate this integral

I am trying to approximate an integral of the following form $$ F_n = \int_{-1}^1(1-u^2)^{(n-3)/2}e^{Anu}du $$ (I am trying to work through this paper....https://ieeexplore.ieee.org/document/6875199) I am just not seeing the substitution I need to…
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What is the meaning and intuition behind Laplace's method for the maximum of a function?

I am reading the book Bandit Algorithms. On page 257, it talks about how to approximate the maximum of a function with Laplace's method. I cannot understand how this method can be used to find the maximum of a function. The book presents Laplace's…
Amin
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How can I find an approximate solution to this integral?

I am stuck in integrating the following integral $I(x) = \int_{a}^{b}t^{2}e^{-xf(t)}\,dt$ where $f(t)=(1-e^{-t})^2$. The main problem here is at the point where $f(t)$ is zero, $t^2$ is zero. I am not sure how to evaluate this integral. Thank you…
Vip
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laplace transform ($t$-shifting)

Find the Laplace transform of: $f(t)=\begin{Bmatrix} \sin (\pi t), & 12 \end{Bmatrix}$ I know how to find the transform by integration of $\sin( \pi t)$ but I'd like to know how to find the transform by using…