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

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SUMMARY

The right-arrow symbol ([itex]\mapsto[/itex]) in stochastic calculus denotes a mapping from time variable t to the integral process defined as \(\int_{0}^t \phi_s dM_s\). This notation indicates that for each value of t, there is a corresponding value of the integral, establishing a continuous local martingale. The discussion clarifies that this representation is standard in the context of defining processes 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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