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Results tagged with stochastic-calculus
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user 81488
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.
5
votes
Accepted
Brownian motion in $\mathbb{R}^n$, probability of hitting a set
It's not that simple. See about polar/nonpolar points/sets e.g. in http://wiki.math.toronto.edu/TorontoMathWiki/index.php/Brownian_Motion_and_Harmonic_functions
If I remember correctly, a set is not …
- 1,897
2
votes
Accepted
Hitting time of a stochastically continuous process
This is not true. Consider some random sequence that converges to $0$ a.s., for example, $Y_n=(Z_1+\cdots+ Z_n)^{-1}$, where $Z$'s are i.i.d. (for instance) Exp(1) random variables. Set
$$
X_t = \beg …
- 1,897
9
votes
Accepted
Brownian motion in $n$ dimensions
The process $\|B(t)\|$ is called $n$-dimensional Bessel process (or Bessel process with parameter $\nu=\frac{n}{2}-1$). I think formula $\bf 4$.1.1.4 of Borodin-Salminen "Handbook of Brownian Motion - …
- 1,897