Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with stochastic-differential-equations
Search options answers only
not deleted
user 8146
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
Existence of strong solution in SDEs and continuity in the time variable
1 and 2 imply linear growth (locally in $t$). Indeed, for any $T>0$ and $t\in[0,T]$
$$
|a(t,x)|\le |a(t,0)| + |a(t,x) - a(t,0)| \le \sup_{s\in[0,T]} |a(s,0)| + K|x|\\\le \big(K\vee ||a(\cdot,0)||_{\in …
- 1,533
9
votes
Accepted
Kolmogorov continuity theorem and Holder norm
One can apply a deterministic result, called Garsia--Rodemich--Rumsey inequality, to estimate $\mathrm{E}[||X||^\alpha_{\gamma;[0,T]}]$. Here is a particular form of this result, which is most conveni …
- 1,533
2
votes
Accepted
Is the "hybrid" Black-Scholes Hull-White model arbitrage free?
The discounted stock price satisfies
$$
dX(t) = \big(\mu(t) - r(t)\big)X(t) dt + \sigma_S(t) X(t) dW_S^{\mathbb P}(t).
$$
The Girsanov density for $X$ is
$$
Z(T) = \exp\left\{\int_0^T \nu(t)dW^{\mat …
- 1,533
2
votes
Smoothness of resolvent of the infinitesimal generator of an Ito diffusion acting on bounded...
It is sufficient that $\inf_x \sigma(x)>0$ and $\sup_x \sigma(x)<\infty$, and $f$ does not have to be monotone. In this case, denoting $\mathcal L f(x) = \frac{1}{2}\sigma(x)f''(x)+\mu(x)f'(x)$, by Th …
- 1,533