New answers tagged stochastic-differential-equations
2
votes
Accepted
Self-adjointness of generator and semigroup of an SDE
Let's at least elaborate on why $P_{s,t} $ in general is not self-adjoint, even if $L_t $ is. $P_{s,t} $ can be composed from infinitesimal time evolutions,
$$
P_{s,t} = \lim_{N\rightarrow \infty } \...
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0
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Simulation of SDEs using Karhunen Loeve expansion
For KL, you need the orthogonality. Simple as that.
If one uses sampling to simulate a stochastic process governed by an SDE (like the Euler-Maruyama you mentioned), one does not need to find such an ...
- 339
4
votes
Accepted
Designing an SDE satisfied by $\frac{B(t)}{1+t}$
The Brownian motion $dX=Adt+DdW$ transforms for $F=f(X,t)$ as
$$dF=\frac{\partial f}{\partial t}(X,t)dt+\frac{\partial f}{\partial x}(X,t)dX+\tfrac{1}{2}D^2\frac{\partial^2 f}{\partial x^2}(X,t)dt.$$
...
- 188k
1
vote
Accepted
What happens to an SDE conditional on the underlying Brownian motion being close to $f \in C[0, T]$?
It is not the case that the support is a singleton in general, and in fact I believe the support will be generically full when the dimension is high enough. I think the full picture is a bit subtle, ...
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