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Captive diffusions and their applications to order-preserving dynamics
(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 ...
Ranking the predictive performances of value-at-risk estimation methods
(Elsevier, 2012)
We introduce a ranking model and a complementary predictive ability test statistic to investigate the forecasting performances of different Value at Risk (VaR) methods, without specifying a fixed benchmark method. The ...
Stochastic sequential reduction of commutative Hamiltonians
(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 ...
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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