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Stochastic calculus provides a consistent theory of integration for stochastic processes and is used to model random systems. Its applications range from statistical physics to quantitative finance.

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Expected value and variance of a stochastic process

First, integrate your SDE. Then you need to use the fact that $v_t$ has Gaussian distribution with mean $m_t$ and variance $n_t$, and apply the expectation to your equation to get the differential equ …
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