Abstract / Description of output
Resetting a stochastic process has been shown to expedite the completion
time of some complex tasks, such as finding a target for the first time. Here we consider the cost of resetting by associating to each reset a cost, which is a function of the distance travelled during the reset event. We compute the Laplace transform of the joint probability of first passage time tf , number of resets N and total resetting cost C, and use this to study the statistics of the total cost and also the time to completion T = C + tf . We show that in the limit of zero resetting rate, the mean total cost is finite for a linear cost function, vanishes for a sublinear cost function and diverges for a superlinear cost function. This result contrasts with the case of no resetting where the cost is always zero. We also find that the resetting rate which optimizes the mean time to completion may be increased or decreased with respect to the case of no resetting cost according to the choice of cost function. For the case of an exponentially
increasing cost function, we show that the mean total cost diverges at a finite resetting rate. We explain this by showing that the distribution of the cost has a powerlaw tail with a continuously varying exponent that depends on the resetting rate.
time of some complex tasks, such as finding a target for the first time. Here we consider the cost of resetting by associating to each reset a cost, which is a function of the distance travelled during the reset event. We compute the Laplace transform of the joint probability of first passage time tf , number of resets N and total resetting cost C, and use this to study the statistics of the total cost and also the time to completion T = C + tf . We show that in the limit of zero resetting rate, the mean total cost is finite for a linear cost function, vanishes for a sublinear cost function and diverges for a superlinear cost function. This result contrasts with the case of no resetting where the cost is always zero. We also find that the resetting rate which optimizes the mean time to completion may be increased or decreased with respect to the case of no resetting cost according to the choice of cost function. For the case of an exponentially
increasing cost function, we show that the mean total cost diverges at a finite resetting rate. We explain this by showing that the distribution of the cost has a powerlaw tail with a continuously varying exponent that depends on the resetting rate.
Original language  English 

Article number  395001 
Pages (fromto)  124 
Number of pages  24 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  56 
Issue number  39 
DOIs  
Publication status  Published  8 Sept 2023 
Keywords / Materials (for Nontextual outputs)
 cost of resetting
 diffusion with resetting
 renewal equation
 stochastic resetting
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The Cost of Stochastic Resetting
Chakanal Sunil, J. (Creator), Edinburgh DataShare, 19 Apr 2023
DOI: 10.7488/ds/3839
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