Browsing by Author "Mengütürk, Murat Cahit"
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Captive diffusions and their applications to order-preserving dynamics
Mengütürk, L. A.; Mengütürk, Murat Cahit (Royal Society Publishing, 2020-09-30)We propose a class of stochastic processes that we call captive diffusions, which evolve within measurable pairs of cadlag bounded functions that admit bounded right-derivatives at points where they are continuous. In full ... -
Captive jump processes for bounded random systems with discontinuous dynamics
Macrina, A.; Mengütürk, L. A.; Mengütürk, Murat Cahit (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, ... -
On a family of coupled diffusions that can never change their initial order
Mengütürk, L. A.; Mengütürk, Murat Cahit (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
Mengütürk, L. A.; Mengütürk, Murat Cahit (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 ... -
Stochastic sequential reduction of commutative Hamiltonians
Mengütürk, L. A.; Mengütürk, Murat Cahit (AIP Publishing, 2020-10-01)This paper introduces a class of stochastic processes constructed by conditioning cadlag processes to take a predetermined set of marginal laws at fixed points in time. We collectively refer to the elements of this class ...
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