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math.PR2023★ 1 cited
Occupied Processes: Going with the Flow
Valentin Tissot-Daguette
A stochastic process becomes occupied when it is enlarged with its occupation flow that tracks the time spent by the path at each level. When is Markov, the o…
math.NA2023
Deep Level-set Method for Stefan Problems
Mykhaylo Shkolnikov, H. Mete Soner, Valentin Tissot-Daguette
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulat…
math.PR2023
Stopping Times of Boundaries: Relaxation and Continuity
H. Mete Soner, Valentin Tissot-Daguette
We study the properties of the free boundaries and the corresponding hitting times in the context of optimal stopping in discrete time. We first prove the continuity of the map fro…