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3
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1answer
138 views

Poisson kernel, expectation, an absolute value comes in

See here. Let $d = 2$, and consider the domain $D = \mathbb{H}$, the upper half-plane. Let $W_t = (X_t, Y_t)$. We see that for any $\theta \in \mathbb{R}$ and any $t \ge 0$, we have$$E^{(x, ...
2
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1answer
128 views

Poisson kernel is the Cauchy distribution, reference?

Let $d = 2$, and consider the domain $D = \mathbb{H}$, the upper half-plane. Can someone give me a reference to a proof that the Poisson kernel is the Cauchy distribution?
2
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2answers
105 views

A question about Skorokhod embedding problem

The Skorokhod Embedding Problem is well known and has many solutions. Now let $B=(B_t)_{t\ge 0}$ be a standard Brownian motion and $\tau$ be an embedding to the centered distribution $\mu$, i.e. the ...
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1answer
88 views

Predictable quadratic Variation <.> has same intervals of constancy as the process

From Revuz and Yor - Continuous Martingales and Brownian Motion 1999 Chapter IV Proposition 1.13 it is proven, that for a continuous local martingale $M_t$ the intervals of ...