Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Reveillac, Anthony"'
In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding representation,
Externí odkaz:
http://arxiv.org/abs/2407.19806
In this paper we develop a representation formula of Clark-Ocone type for any integrable Poisson functionals, which extends the Poisson imbedding for point processes. This representation formula differs from the classical Clark-Ocone formula on three
Externí odkaz:
http://arxiv.org/abs/2404.07541
In this paper we fill a gap in the literature by providing exact and explicit expressions for the correlation of general Hawkes processes together with its intensity process. Our methodology relies on the Poisson imbedding representation and on recen
Externí odkaz:
http://arxiv.org/abs/2304.02376
We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals with respect to Hawkes processes by a normally distributed random variable. In the case of deterministic and non-negative integrands, our estimate
Externí odkaz:
http://arxiv.org/abs/2209.03621
We introduce and study an alternative form of the chaotic expansion for counting processes using the Poisson imbedding representation; we name this alternative form \textit{pseudo-chaotic expansion}. As an application, we prove that the coefficients
Externí odkaz:
http://arxiv.org/abs/2209.01972
In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between functionals of a compound Hawkes process and a given Gaussian density. To achie
Externí odkaz:
http://arxiv.org/abs/2104.01583
In this paper we provide an expansion formula for Hawkes processes which involves the addition of jumps at deterministic times to the Hawkes process in the spirit of the well-known integration by parts formula (or more precisely the Mecke formula) fo
Externí odkaz:
http://arxiv.org/abs/2104.01579
We investigate Weierstrass functions with roughness parameter $\gamma$ that are H\"older continuous with coefficient $H={\log\gamma}/{\log \frac12}.$ Analytical access is provided by an embedding into a dynamical system related to the baker transform
Externí odkaz:
http://arxiv.org/abs/2009.03628
In this paper we provide an It{\^o}-Tanaka-Wentzell trick in a non semimartingale context. We apply this result to the study of a fractional SDE with irregular drift coefficient.
Externí odkaz:
http://arxiv.org/abs/1907.03629
Publikováno v:
In Stochastic Processes and their Applications February 2023
