Mario Lefebvre, "Homing Problems for Diffusion Processes with Random Resettings," WSEAS Transactions on Mathematics, vol. 25, pp. 269-273, 2026, DOI:10.37394/23206.2026.25.27
Mario Lefebvre. Homing Problems for Diffusion Processes with Random Resettings.
WSEAS Transactions on Mathematics. 2026;25:269-273. 10.37394/23206.2026.25.27
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Homing Problems for Diffusion Processes with Random Resettings
Author:
Abstract: The problem of minimizing the expected time spent by one-dimensional stochastic processes in a given
interval is considered in the case of diffusion processes with random resettings. At random times that occur
according to a Poisson process, the controlled diffusion process jumps from its current position to a fixed value.
The differential equation satisfied by the value function is given and particular problems are solved explicitly.
Keywords:
Wiener process, stochastic control, dynamic programming, jump-diffusion process, special functions, integro-differential equation
Pages: 269-273 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 25, 2026, Art. #27 DOI: 10.37394/23206.2026.25.27
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