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Results tagged with stochastic-calculus
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user 172746
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.
2
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1
answer
736
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Mean square derivatives and modifications
Suppose we have a stochastic process $X$ on $\mathbb{R}$. Suppose there exists a stochastic process $\frac{d X(t)}{d t}$ such that
$$\lim_{h\to0} \mathbb{E}\left[\left(\frac{X(t+h)-X(t)}{h}-\frac{d X( …
- 151
3
votes
2
answers
940
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Regarding sample continuity of Gaussian Processes
Suppose we have a Gaussian Process $X_t$ on $\mathbb{R}^n$ with mean function $m(t)$ and covariance function $K(t,s)$. Then is $X_t$ being sample continuous (i.e. the sample paths of $X_t$ are almost …
- 151