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On a family of coupled diffusions that can never change their initial order
(IOP Publishing, 2022-11-18)
We introduce a real-valued family of interacting diffusions where their paths can meet but cannot cross each other in a way that would alter their initial order. Any given interacting pair is a solution to coupled stochastic ...
Piecewise-tunneled captive processes and corridored random particle systems
(Springer, 2023-01)
We introduce a family of processes that generalises captive diffusions, whereby the stochastic evolution that remains within a pair of time-dependent boundaries can further be piecewise-tunneled internally. The tunneling ...
Captive jump processes for bounded random systems with discontinuous dynamics
(Elsevier, 2024-01)
Stochastic captive jump processes are explicitly constructed in continuous time, whose non-linear dynamics are strictly confined by bounded domains that can be time-dependent. By introducing non-anticipative path-dependency, ...
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