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Mar 4, 2018 at 7:00 comment added Paul No worries... not like there’s carried interest :)
Feb 28, 2018 at 16:02 comment added john_w lol, sorry about the long wait to select your answer. It has almost been two years lol.
Feb 17, 2018 at 8:39 vote accept john_w
Dec 24, 2016 at 6:19 history bounty ended CommunityBot
Dec 19, 2016 at 5:35 comment added Paul @john w, if you think the answer was satisfactory, would you please consider selecting it as the correct answer?
Dec 18, 2016 at 20:16 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 19:26 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 19:01 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:46 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:39 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:30 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:25 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:12 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 18:02 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 16:52 history edited Paul CC BY-SA 3.0
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Dec 16, 2016 at 16:52 comment added Paul Hi John, thanks for the catch, I have edited accordingly. As for your first comment: you're right that I wasn't being very precise. In fact, the concept I am taking advantage of here is that of a filtration, which basically stands for the sum total of all information available up to time t. I will add a more detailed explanation of this to my answer.
Dec 16, 2016 at 7:05 comment added john_w Also sorry do you mean $T_1 = k$ instead of $T_1=n$ in your second "Probability" on the right-hand side of the Law of Total Expectation?
Dec 16, 2016 at 7:03 comment added john_w Hi Paul, the Markov Property I was reading says something above the conditional probability of $X_j$ where $X_j$ is the state of $X$ at time $j$. But it doesn't say anything about the "time that we First Reaches state s", i.e. it doesn't say whether $T_s$ exhibits Markov Property. But it seems the author is trying to say it is using "Markov Property" on the $T_s$.
Dec 16, 2016 at 5:44 history answered Paul CC BY-SA 3.0