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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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 …
VictorZurkowski's user avatar
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 …
VictorZurkowski's user avatar
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 …
VictorZurkowski's user avatar
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 …
VictorZurkowski's user avatar
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 …
VictorZurkowski's user avatar