6 papers
Absolute continuity of Rosenblatt measures
Petr Čoupek, Tyrone E. Duncan, Bozenna Pasik-Duncan +1
In the article, we address the problem of absolute continuity of translated Rosenblatt measures on the path space. In [Čoupek, P., Kříž, P., Maslowski, B., Stoch. Proc. Appl. 179 (…
Mean-Field-Type Game Theory with Rosenblatt Noise
Hamidou Tembine, Tyrone E. Duncan, Bozenna Pasik-Duncan
We study the integration of Rosenblatt noise into stochastic systems, control theory, and mean-field-type game theory, addressing the limitations of traditional Gaussian and Markov…
Semi-Explicit Solution of Some Discrete-Time Higher-Order-Cost Mean-Field-Type Control
Julian Barreiro-Gomez, Tyrone E. Duncan, Bozenna Pasik-Duncan +1
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities i…
Semi-Explicit Solution of Some Discrete-Time Mean-Field-Type Games with Higher-Order Costs
Julian Barreiro-Gomez, Tyrone E. Duncan, Bozenna Pasik-Duncan +1
Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they…
A Stochastic Calculus for Rosenblatt Processes
Petr Čoupek, Tyrone E. Duncan, Bozenna Pasik-Duncan
A stochastic calculus is given for processes described by stochastic integrals with respect to fractional Brownian motions and Rosenblatt processes somewhat analogous to the stocha…
Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Method
Julian Barreiro-Gomez, Tyrone E. Duncan, Bozenna Pasik-Duncan +1
This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These inc…