New answers tagged stochastic-processes
1
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What is the expected remaining life duration of a cell in the $t\to\infty$ limit?
I don't agree. I think the exponential growth biases it towards younger individuals, that is, lots of newborns. My back of the envelope calculation is the following. Suppose the distribution of ...
1
vote
Optimally betting a beta-biased coin
Let $\alpha_0$ bet the cutoff value of $\alpha$ as a function of $N$ and $\beta$ -- meaning that for $0<\alpha<\alpha_0$ it is better not to bet on the first coin flip while for $\alpha_0<\...
1
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A coupon collector-ish question
Here's a not quite complete argument:
Let $t$ be the number of (not necessarily distinct) coupons you've seen so far. For a given coupon, the probability you have not seen it so far is $(1-p_i)^t$. ...
6
votes
The drunken blind man’s walk
The expected exit time (from a ball of radius 1) is $(1+o_\delta(1))/\delta^2$, regardless of the choice of strategy (the $o_\delta(1)$ term does depend on the strategy). Indeed, write $X_n=\sum_{i=1}^...
0
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Does point process ordering ever imply conditional intensity ordering?
I am placing this as a partial answer here rather than a new question or editing the question.
I have found a counterexample where $N\subset_{st}N'$ but the conditional intensities are not ordered. I ...
4
votes
Accepted
Construction of random tempered distributions
Let me replace $\mathbb{R}_+\times \mathbb{R}^d$ by $\mathbb{R}$, the generalisation is an easy exercise. Write $\phi_n$ for the $n$th Hermite function, so that $\eta_n = \xi_{\phi_n}$ form a sequence ...
4
votes
Accepted
Decay estimate of moment of an SDE
Since we can apply Burkholder-Davis-Gundy to control the supremum of moments, we start by removing the tail simply using $1\leq \frac{|X_{t}|}{R}$.
$$
\mathbb E [ |X_t|^p 1_{\{|X_t| \ge R\}} ]\leq \...
3
votes
If Kolmogorov continuity criterion gives the optimal Hölder regularity then does the process have all moments?
I believe that the answer is "no", here is almost a proof. Take $\tau_n$ to be an i.i.d. sequence of uniform $[0,1]$ random variables and take $Z_n$ an i.i.d. sequence of random variables ...
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