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- End Point: The "point" at which a line or curve ends.
www.thoughtco.com/glossary-of-mathematics-definitions-4070804Math Glossary: Over 150 Mathematics Terms Defined - ThoughtCo
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May 18, 2015 · The definition I am provided with is as follows: A random time $τ$ is called a stopping time if for any $n$, one can decide whether the event $\ {τ ≤ n\}$ (and hence the complementary event $\ {τ > n\}$) has occurred by observing the first n variables $X_1, X_2, . . . , X_n$.
Apr 23, 2022 · In a sense, a stopping time is a random time that does not require that we see into the future. That is, we can tell whether or not \( \tau \le t \) from our information at time \( t \). The term stopping time comes from gambling. Consider a gambler betting on games of chance.
Given an implication of the form $P \rightarrow Q$, the statement $Q \rightarrow P$ is known as its converse. For example: The converse of “if $f (x)\ge 2$, then $f (x)^2\ge 4$” is “$f (x)^2\ge 4$, then $f (x)\ge 2$.”. The converse of “all composite integers are odd” is “all odd integers are composite.”.
6.2 Stopping Times Let (Ω,F,P) be a probability space and let (F t) t⩾0 be a filtration of (Ω,F,P). Definition 6.8.A random variable T : Ω →[0,∞] is called a stopping time w.r.t. the filtration (F t) t⩾0 if {T⩽t}∈F t for all t⩾0. Consequently, if Tis a (F t) t⩾0 stopping time, then {T<t}= [∞ n=1 ˆ T⩽t− 1 n ˙ ∈F t ...
May 2, 2024 · Use this glossary of over 150 math definitions for common and important terms frequently encountered in arithmetic, geometry, and statistics.
Apr 23, 2022 · Recall that a random time \( \tau \) with values in \( T \cup \{\infty\} \) is a stopping time relative to \( \mathfrak F \) if \( \{\tau \le t\} \in \mathscr{F}_t \) for \( t \in T \). So a stopping time is a random time that does not require that we see into the future.
A stopping time is often defined by a stopping rule, a mechanism for deciding whether to continue or stop a process on the basis of the present position and past events, and which will almost always lead to a decision to stop at some finite time.
