\(
\mathbf{P}_{x, t} [\Lambda_s] := \dfrac{\mathbf{E}_x [e^{A_t} \mathbf{1}_{\Lambda_s}]}{\mathbf{E}_x [e^{A_t}]}, \quad \mathbf{P}_{x, \infty } [\Lambda_s] {=} \mathbf{E}_x [\mathbf{1}_{\Lambda_s} M_s]?
\)
\( M_s \) is a multiplicative martingale.
参考：
はてなブログ以外でMathJaxを使う場合
https://a-habakiri.hateblo.jp/entry/2016/12/24/163136
MathJax
https://www.mathjax.org/
