## On hitting times of conditioned diffusions

I have a question of a conditioned diffusion processes. This question is somewhat related to an argument which appears in this paper: P.

Let $$D=\{z=(x,y) \in \mathbb{R}^2 \mid |y|<1\}$$ and $$K=\{(x,y) \in D \mid x<1\}$$. We denote $$X=(X_t,P_z)$$ by the absorbing Brownian motion on $$D$$ conditioned to hit $$K$$. We let $$T_{K}=\inf\{t \ge 0 \mid X_t \in K\}$$.

My question

We set $$S=\inf\{t \ge 0 \mid \text{ the second coordinate of }X_{t}=-1/2\}$$.

Can we prove the following?: \begin{align*} (1) \quad \lim_{x \to +\infty}\inf_{z=(x,y) \in D \ \text{ with }-1/2

A claim similar to (1) should hold for more general conditioned diffusions on $$D$$. Can we prove (1) with some universal argument? I would like to know whether similar claims to (1) can be proved for more general conditioned diffusions.

## Implicit “Submit” after hitting Done on the keyboard at the last EditText [on hold]

I’ve used some apps where when I fill my username, then go to my password, if I hit “Done” on the keyboard, the login form is automatically submitted, without me having to click the submit button. How is this done? I use Kotlin language.

## Probability of Random walk with 2 absorbing walls hitting one wall during N steps

Assume a i.i.d. one dimensional random walk S with symmetrical probabilities of 1/2 for a unit plus or minus step. Start is at S = 0 and absorbing walls are at S = – B and S = + A. What is the probability Pa that the particle will be absorbed at S = A before reaching S = – B or escaping unabsorbed during or by N steps. Assume N > 2A + B and assume if necessary A > B.

What is the probability Pu that the particle hits neither wall in N steps?

The solution for N -> infinity or until particle is absorbed is Pa = b / a + b. But for finite N this is solved tediously by counting outcomes for specific cases. Can anyone find a closed solution for Pa in terms of A, B and N?

This is called Gambler’s Ruin.

## Hitting probability of a transient diffusion process

I have a question about properties of transient diffusion process.

In the case of $$d$$-dimensional Brownian motion $$B=(B_t,P_x)$$ ($$d \ge 3$$), we can prove that \begin{align} (1)&\quad 0 Here, $$K$$ is a compact subset of $$\mathbb{R}^d$$ with positive Lebesgue measure and $$\sigma_{K}=\inf\{t \ge0 \mid X_t \in K\}$$. $$|\cdot|$$ is the Eucledean metric. Note that (2) follows from the heat kernel estimate of the Brownian motion and the strong Markov property.

My question

We consider the next diffusion $$X=(X_t,P_x)$$ on $$\mathbb{R}^d$$: $$\begin{equation*} X_t=x+\int_{0}^{t}a(X_s)\,dB_s+\int_{0}^{t}b(X_s)\,ds, \end{equation*}$$ where $$a$$ and $$b$$ are bounded continuous functions on $$\mathbb{R}^d$$ and $$B$$ is the $$d$$-dim Brownian motion starting from the origin. We assume that $$X$$ is transient.

Is there conditions on $$a$$ and $$b$$ such that $$\inf_{x \in \mathbb{R}^d}P_{x}(T_{K}<\infty)>0?$$

Here, $$T_K=\inf\{t>0 \mid X_t \in K\}$$.

## Does hitting a creature with a magical creature counts as magical damage?

Half-Orc Barbarian Conan has been Enlarged, making him Large. During a fight against some Couatls, he managed to grappled one and beat it to death.

Now, having already something (the body of the dead Couatl) in his hands and being a tad affected by its current rage, Conan decides to strike a second Couatl with the first one. Laughs all around the table as the DM rules that he can indeed wield the corpse as an improvised weapon (bludgeoning), given the situation.

A Couatl is immune to non-magical bludgeoning, among other things. But given the fact that the first Couatl is a magical creature and has the Magic Weapons feature, does the damage counts as magical damage?

Magic Weapons: The couatl’s weapon attacks are magical.

If yes, would any “magical creatures” work for this purpose or only ones with the Magic Weapons feature?

## Are these new “featured content” hitting your web traffic too?

Are these new "featured content" hitting your web ranks too?

It seems like google is indexing our webpages,
scrapping our content,
and displaying it on their own website.

Complete answers to various questions are getting posted there…
If people are getting answers directly on google website, then who would come to our website?

We are the ones who made that content, are paying for servers, and other services,
and its google which is getting the traffic…

Yesterday I was looking for…

Are these new "featured content" hitting your web traffic too?