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Results tagged with stochastic-processes
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user 116983
A stochastic process is a collection of random variables usually indexed by a totally ordered set.
4
votes
1
answer
244
views
Infinite-time, Path-Dependent Expected Value of an Orstein-Uhlenbeck process
I am dealing with an Orstein-Uhlenbeck process $X_t$ with its stochastic differential equation being
$$dX_t=(\mu-X_t)dt+\sigma dW_t.$$
I want to show
$$\mathbb{E}\left[\frac{|X_\infty|}{\int_{0}^{\ …
- 389
5
votes
2
answers
889
views
Itô's Formula for functions that are $C^2$ almost everywhere
In the conventional Itô's formula, it is required that $F$ is $C^2$ everywhere. However I've seen mentioning of a slightly weaker condition, where $F$ is $C^1$ everywhere but $C^2$ almost everywhere. …
- 389