Wald for non-stopping times: the rewards of impatient prophets
نویسندگان
چکیده
منابع مشابه
Wald for non-stopping times: The rewards of impatient prophets
Let X1, X2, . . . be independent identically distributed nonnegative random variables. Wald’s identity states that the random sum ST := X1 + · · · + XT has expectation ET ·EX1 provided T is a stopping time. We prove here that for any 1 < α ≤ 2, if T is an arbitrary nonnegative random variable, then ST has finite expectation provided that X1 has finite α-moment and T has finite 1/(α− 1)-moment. ...
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ژورنال
عنوان ژورنال: Electronic Communications in Probability
سال: 2014
ISSN: 1083-589X
DOI: 10.1214/ecp.v19-3609