3 citations · 5 across the 5 of their papers we have counts for
6 papers
Functional Laws of Large Numbers for Marked Hawkes Processes and Compound Marked Hawkes Processes
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz iewȩgłowski +1
We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement…
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…
Conditional Markov Chains Part II: Consistency and Copulae
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
In this paper we continue the study of conditional Markov chains (CMCs) with finite state spaces, that we initiated in Bielecki, Jakubowski and Niewęgłowski (2015). Here, we turn o…
Jump-diffusion processes in random environments
Jacek Jakubowski, Mariusz Niewęgłowski
In this paper we investigate jump-diffusion processes in random environments which are given as the weak solutions to SDE's. We formulate conditions ensuring existence and uniquene…
Intricacies of Dependence between Components of Multivariate Markov Chains: Weak Markov Consistency and Markov Copulae
Tomasz R. Bielecki, Jacek Jakubowski, Mariusz Niewęgłowski
This article continues our study of Markovian consistency and Markov copulae. In particular, we characterize the weak Markovian consistency for finite Markov chains. We discuss som…
Defaultable bonds with an infinite number of Levy factors
Jacek Jakubowski, Mariusz Nieweglowski
A market with defaultable bonds where the bond dynamics is in a Heath-Jarrow-Morton setting and the forward rates are driven by an infinite number of Levy factors is considered. Th…