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Results tagged with pr.probability
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user 47322
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Regularity of finite variation kernels in the (intersection) of the semimartingale spaces $H^p$
If the answer to Question 1 was affirmative, then it would be the case when M = 0 and b is deterministic, and it would imply L$^1$[0,t] $\subset$ L$^p$[0,t] (for any finite t >0), which is not true if …
- 489
4
votes
Wasserstein distance in R^d from one dimensional marginals
PS: I posted an answer in 2015. In late 2019, @Neyman identified a problem with my original post.
Here is a non-constructive answer to the question.
I don't know of any reference where you can f …
- 489
3
votes
Accepted
Stochastic integration by parts to obtain Kailath Segall identity for iterated stochastic in...
The case $n=1$ is straighfoward. Now, applying Ito's formula and the definition of $\{I_n\}$ to integrate by parts we have:
\begin{align*}
I_n = \int_0^t I_{n-1} (s) \ d M_s = I_{n-1}M - \int_0^t I …
- 489
1
vote
Accepted
Smooth Approximation of Indicator Function of Convex Sets in $\mathbb{R}^n$
Let's pursue Jochen's idea. We assume $A \ne \emptyset.$
Let
$$ \varphi(t) = \begin{cases}
e^{-\frac{1}{t}} &\text{if $ t>0$}\\
0 &\text{otherwise.}
\end{cases}$$
This func …
- 489
1
vote
Weak convergence of sum of log normal random variables
For each i, $S_{t_i}$ is distributed as $exp( (r - \sigma^2/2)t_i + Z \sqrt{t_i})$, where $Z$ is a standard normal. If we take $S^k_{t_i} = exp( (r - \sigma^2/2)t_i + Z \sqrt{t_i})$ for all k and i, t …
- 489