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math.PR2020
Generalized Multivariate Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Nieweglowski
This work contributes to the theory and applications of Hawkes processes. We introduce and examine a new class of Hawkes processes that we call generalized Hawkes processes, and th…
math.PR2018
Semimartingales and Shrinkage of Filtration
Tomasz R. Bielecki, Jacek Jakubowski, Monique Jeanblanc +1
We consider a complete probability space , which is endowed with two filtrations, and , assumed to satisfy the usual conditions…
math.PR2011★ 3 cited
On some Brownian functionals and their applications to moments in lognormal and Stein stochastic volatility models
Jacek Jakubowski, Maciej Wisniewolski
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a pro…