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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
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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.
Oct
22
asked Processes approximating a reflected brownian motion.