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Aug
20 |
awarded | Nice Question |
Jul
2 |
awarded | Curious |
May
4 |
accepted | Usefulness of Frechet versus Gateaux differentiability or something in between. |
May
4 |
awarded | Nice Question |
Oct
9 |
awarded | Popular Question |
Dec
2 |
comment |
total variation distance between two solutions of SDE
Those random variables have distribution functions which are discontinuous. |
Dec
1 |
comment |
total variation distance between two solutions of SDE
Yeah but your construction of $\mu$ and $\nu$ is a weak one, in that it says nothing about dependence on particular values of $\omega \in \Omega$. Using Grownwall's inequality you can get a convergence rate for (strong) $L^1$ convergence, $E \left|X_t^1 - X_t^2 \right|$ tends to zero in some sense. This implies total variation convergence. |
Dec
1 |
comment |
total variation distance between two solutions of SDE
Isn't a bound on $|X_t^1 - X_t^2|$ considerably stronger than a bound in total variation distance? One is strong and the other is weak? |
Nov
29 |
awarded | Critic |
Nov
19 |
comment |
Properties of the Euler Discretization of a diffusion
Also, do you know any general references about convergence properties for optimal stopping problems? For example, the above kind of uniform convergence is something I need, but by itself does not imply convergence of optimal stopping, since i.e. hitting times aren't continuous with respect to the uniform norm. |
Nov
19 |
comment |
Properties of the Euler Discretization of a diffusion
Thanks, this is the convergence that I was most interested in. Do you have a reference for this fact, and is the convergence rate $O(t)$? |
Nov
17 |
comment |
Properties of the Euler Discretization of a diffusion
Thanks for your answer. It seems like strong convergence doesn't have much to say about convergence of optimal stopping problems, unless you can leverage some additional information, like martingality, to use a maximal inequality. Kloeden/Platen also don't have anything to say about this. Do you know of anything in this direction? |
Nov
17 |
asked | Properties of the Euler Discretization of a diffusion |
Jul
3 |
revised |
Compactness of the set of densities of equivalent martingale measures
added 9 characters in body |
Jul
3 |
answered | Compactness of the set of densities of equivalent martingale measures |
Jun
14 |
answered | Blackbox Theorems |
Mar
27 |
awarded | Popular Question |
Dec
5 |
awarded | Yearling |
Oct
23 |
comment |
Processes approximating a reflected brownian motion.
One thought: the reflected BM is a standard BM plus a local time term at zero. Using the interpretation of local time in terms of downcrossings should possibly do the trick. |
Oct
23 |
comment |
Processes approximating a reflected brownian motion.
Thanks for the reference, will take a look. |