arXiv subjects
Publications and source records attributed to Dmytro Karabash.
This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with an example of application in finance.
Existence and stability properties are studied for Hawkes process, i.e. point process $S$ that has long-memory and intensity $r(t)=λ\big(g_0(t)+ \sum_{τ<t, τ\in S} h(t-τ) \big)$. The approach to Hawkes process presented in this paper allows us to prove the uniqueness of invariant distribution of the process under weaker conditions. New speed of convergence results are also shown. Unlike previous results the function $λ$ is not required to be Lipschitz and can be even discontinuous. Some generalizations are also considered.
The Sarkar-Wang algorithm computes the hat version of the Heegaard Floer homology of a closed oriented three manifold. This paper analyzes the computational complexity of the Sarkar-Wang algorithm; then the algorithm is modified to obtain a better bound. Then the computational complexity of calculating HFK hat from a Heegaard diagram by means of the modified Sarkar-Wang algorithm is also analyzed. Under certain assumptions it is shown that the modified Sarkar-Wang algorithm is faster than the Manolescu-Ozsvath-Sarkar algorithm.