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votes
0answers
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integral related to Gaussian random variable and Brownian Motion
This integral arises from some work I am doing related to Brownian motion.
The integral of interest is the following
$\int^{\infty}_{t=0}\int^{b}_{x=-\infty}\frac{1}{\sqrt{2\pi ...
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2answers
236 views
Partial Derivative of an Integral
If $f(t)$ is a deterministic function of $t$ and $B_{n}$ is a brownian motion and:
$Z =\int^t_0 f(s)dB(s)$
How does one take the partial derivatives wrt to $t$ and $B_n$ on an integral like this?
I ...
4
votes
1answer
624 views
How to derive the Ornstein-Uhlenbeck Stochastic Integral Equation?
I have a question regarding the Ornstein -Uhlenbeck process. We have a simplified version with Stochastic Integral Equation: $X_t=-a\int^t_0 X_s\,ds +B_t$. B is the Brownian motion.
And its analytic ...
