Strange right-arrow symbol ([itex]\mapsto[/itex]) in stochastic calculus.

AI Thread Summary
The right arrow symbol ([itex]\mapsto[/itex]) in the context of stochastic calculus indicates a mapping from time variable t to the integral process defined as [itex]\int_{0}^t \phi_s dM_s[/itex]. This notation signifies that for each value of t, there is a corresponding value of the integral, establishing a continuous local martingale. The discussion clarifies that this mapping is well-defined and relates to the quadratic variations of the process. Overall, the symbol serves to illustrate the relationship between the time variable and the resulting stochastic process. Understanding this notation is crucial for interpreting the properties of martingales in stochastic calculus.
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What does the right arrow mean in this context:

"
...Then the process t \mapsto \int_{0}^t \phi_s dM_s are well-defined continuous local martingales, whose quadratic variations are given by ...

"

Is this supposed to mean "the process X that is the mapping X: t \mapsto \int_{0}^t \phi_s dM_s"
 
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Yes, that indicates a "mapping". t is mapped to \int_0^t \phi_s dM_s.
 

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