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First Passage (FP) processes are utilized widely to model phenomena in manyareas of mathematical applications, from biology to computer science.Introducing a mechanism to restart the parent process can alter the firstpassage characteristics, and the properties of the resulting First PassageUnder Restart (FPUR) process have been subject to much recent investigation.Here we seek to more fully characterize whether a discrete FP process can haveits mean hitting time reduced through the implementation of restart byanalyzing a construct we call the restart sequence, which is determined solelyby the distribution of the FP process.

Using Restart Sequences to Determine Beneficial First Passage Under Restart