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Jul
2
awarded  Curious
May
5
awarded  Tumbleweed
Apr
28
asked Condition on initial value of stochastic process
Mar
12
comment Differentiability of function defined as integral
Nice. Thank you very much. Is there any way to determine the (non-)differentiability of $F$ without actually computing $$\int_0^1 \frac{f(t,h) - f(t,0)}{h} dt$$ ? My question is coming from a real problem where I can compute derivatives of $f$ w.r.t $x$ but cannot explicitly integrate $f$ w.r.t $t$.
Mar
12
accepted Differentiability of function defined as integral
Mar
11
asked Differentiability of function defined as integral
Sep
12
asked Ito vs Stratonovich SDE with irregular time-dependence in coefficients
Jul
2
comment Prove the density of this SDE is not smooth in a parameter
thank you for your answer. I don't quite see how it helps with determining smoothness in the variable $x$, though.
Jun
28
awarded  Promoter
Jun
26
asked Prove the density of this SDE is not smooth in a parameter
Apr
9
answered Martingale inequality
Apr
7
comment Martingale inequality
Well, the inequality holds for all fixed $r$. And, assuming $f$ is continuous in the first variable, I think that for a given $t$, $Y^r_t$ and $Y^t_t$ should be close when $r$ is close to $t$. However, I am not sure if the same is true of $\sup_{t \in [0,T]} Y^r_t$ and $\sup_{t \in [0,T]} Y^t_t$ or the quadratic variations.
Apr
7
comment Martingale inequality
@Did I have found a reference: see proposition 4.24 here statslab.cam.ac.uk/~beresty/teach/StoCal/sc3.pdf
Apr
7
comment Martingale inequality
@Did My source is a paper by Kusuoka & Stroock (Applications of the Malliavin calculus. II) which is not available online, but the inequality comes from viewing the martingale as Brownian Motion run at the "clock" of its quadratic variation, using the distribution the running max of a Brownian Motion and using Gaussian tail estimates.
Apr
6
asked Martingale inequality
Aug
29
accepted Roll six dice. Probability of at least one pair.
Aug
29
asked Roll six dice. Probability of at least one pair.
Jun
18
awarded  Commentator
Jun
18
comment Are affine SDEs invertible?
@mike : Sorry, I see what you are saying now. Do you have a reference for proving that say $X_t = x + \int_0^t a_s ds + \int_0^t b_s dW_s$ hits zero a.s.?
Jun
15
comment Are affine SDEs invertible?
@mike : In 1-d this is a geometric Brownian motion, so does not hit zero.