Author: "Privault, Nicolas" / Language: english / Publication Year Range: Last 3 years / Topic: point processes - Searchworks@Jio Institute Digital Library Search Results

Your search keyword '"Privault, Nicolas"' showing total 2 results

Start Over Author "Privault, Nicolas" Topic point processes Publication Year Range Last 3 years Language english

Author: Privault, Nicolas
Subjects: *POISSON processes, *POINT processes, *RANDOM sets, *POINT set theory, *POISSON distribution, *STOCHASTIC geometry, *MARTINGALES (Mathematics)
Abstract: We construct unbiased estimators for the distribution of the number of points inside random stopping sets based on a Poisson point process. Our approach is based on moment identities for stopping sets, showing that the random count of points inside the complement S̅ of a stopping set S has a Poisson distribution conditionally to S. The proofs do not require the use of set-indexed martingales, and our estimators have a lower variance when compared to standard sampling. Numerical simulations are presented for examples such as the convex hull and the Voronoi flower of a Poisson point process, and their complements. [ABSTRACT FROM AUTHOR]
Published: 2021
Full Text: View/download PDF

Author: Privault, Nicolas
Subjects: *MONTE Carlo method, *CUMULANTS, *DIFFERENTIAL equations, *POINT processes, *MARTINGALES (Mathematics)
Abstract: We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes. [ABSTRACT FROM AUTHOR]
Published: 2021
Full Text: View/download PDF

Books, media, physical & digital resources

Searchworks