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 not deleted
user 22157
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.
4
votes
A Stochastic Taylor Expansion/Asymptotics
Write $f(t) := \mathbb E \left[ \exp\left( - \int_0^t r_s \ d s \right) \right]$. Define stochastic processes $y_t = \exp \left( -\int_0^t r_s \ d s \right)$ and $z_t = r_t y_t$. Then
$y_t = 1 - \int_ …
- 985
3
votes
Accepted
Girsanov theorem and the density of a process
Short answer: it follows directly from the Radon-Nikodym theorem.
Longer answer: Let $\mu$ denote the law of $Y(t)$ under $\mathbb P_{y_0}$ and let $\nu$ denote the law of $Y(t)$ under $\mathbb Q_{y_ …
- 985
3
votes
Accepted
Computing transition operators for Markov processes
1) Explicit expressions for transition densities
In the case of linear systems with additive noise of the form
$d X(t) = (A X_t + b) \, d t + \sigma \, d B_t$
it is possible to obtain an explicit …
- 985
1
vote
Limit of first passage time
The key thing is that your diffusion is Feller under the stated conditions, so $x \mapsto \mathbf E_x f(X_t)$ is continuous. Therefore $x \mapsto \int_0^{\infty} \mathbf E_x f(X_t) e^{-rt} \ d t$ is c …
- 985