Search results
Results From The WOW.Com Content Network
Suppose further that the walk stops if it reaches 0 or m ≥ a; the time at which this first occurs is a stopping time. If it is known that the expected time at which the walk ends is finite (say, from Markov chain theory), the optional stopping theorem predicts that the expected stop position is equal to the initial position a.
Example of a stopping time: a hitting time of Brownian motion.The process starts at 0 and is stopped as soon as it hits 1. In probability theory, in particular in the study of stochastic processes, a stopping time (also Markov time, Markov moment, optional stopping time or optional time [1]) is a specific type of “random time”: a random variable whose value is interpreted as the time at ...
For convenience (see the proof below using the optional stopping theorem) and to specify the relation of the sequence (X n) n∈ and the filtration (F n) n∈ 0, the following additional assumption is often imposed:
The concept of a stopped martingale leads to a series of important theorems, including, for example, the optional stopping theorem which states that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial value.
Maxwell's theorem (probability theory) Optional stopping theorem (probability theory) Poisson limit theorem (probability) Raikov's theorem (probability) Skorokhod's embedding theorem ; Skorokhod's representation theorem ; Slutsky's theorem (probability theory) Theorem of de Moivre–Laplace (probability theory)
Optimal stopping problems can be found in areas of statistics, economics, and mathematical finance (related to the pricing of American options). A key example of an optimal stopping problem is the secretary problem.
What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value? The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent, that is, the optimal rule depends at every stage on all preceding values, and not ...
What links here; Related changes; Upload file; Permanent link; Page information; Cite this page; Get shortened URL; Download QR code