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Results tagged with stochastic-differential-equations
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user 51335
Stochastic ordinary and partial differential equations generalize the concepts of ordinary and partial differential equations to the setting where the unknown is a stochastic process.
2
votes
0
answers
137
views
Lebesgue Integral in SDE
In the context of proving existence of solutions of S(P)DEs, I've found that few (if any) texts offer significant mention to the deterministic drift term of the form
$$
\int_0^t f(s,X(s))ds.
$$
If we …
- 379
3
votes
0
answers
88
views
Generators and Covariance Operators of Diffusions
For a constant coefficient Ornstein-Uhlenbeck process, how should I think about the relationship between the infinitesimal generator of the process and the covariance operator of the process (or, equi …
- 379
1
vote
0
answers
57
views
Choice of Banach space for stochastic processes
In studying $X$ (Banach space) valued stochastic processes, I tend to see two different norms used:
$$
\sup_{t\leq T} \mathbb{E}[\|u(t)\|_{X}^p]^{1/p}
$$
and
$$
\mathbb{E}[\sup_{t\leq T} \|u(t)\|_X^p] …
- 379
5
votes
2
answers
909
views
Analytic Solution to SDEs
Are there any example of SDEs with constant diffusion terms, other than the Ornstein Uhlenbeck process, which have exact solutions? I'm thinking of something of the form:
\begin{equation}
dX_t = f(X_ …
- 379