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- E. Bacry, S. Delattre, M. Hoffmann, J. F. Muzy
- 2011

We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] in the limit T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with… (More)

- E. Bacry, S. Delattre, M. Hoffmann, J. F. Muzy
- 2011

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative… (More)

We model the growth of a cell population by a piecewise deter-ministic Markov branching tree. Each cell splits into two offsprings at a division rate B(x) that depends on its size x. The size of each cell grows exponentially in time, at a rate that varies for each individual. We show that the mean empirical measure of the model satisfies a… (More)

- E. Bacry, S. Delattre, M. Hoffmann
- 2010

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the… (More)

PURPOSE
The goal of this work was to assess the effect of comorbidities on medical care use and costs among patients with partial seizure disorder who are also refractory to initial antiepileptic drug (AED) monotherapy.
METHODS
Retrospective data from the PharMetrics managed care claims database were collected for adult patients treated with AED… (More)

Many organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger a cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size… (More)

- E. Bacry, S. Delattre, M. Hoffmann
- 2013

In the context of statistics for random processes, we prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] when T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the… (More)

- S. Delattre, M. Hoffmann
- 2012

We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a… (More)

- Marc Hoffmann
- 2008

We explore statistical inference in self-similar conservative fragmentation chains, when only (approximate) observations of the size of the fragments below a given threshold are available. This framework , introduced by Bertoin and Martinez, is motivated by mineral crushing in mining industry. The underlying estimated object is the step distribution of the… (More)

- MARC HOFFMANN, MARKUS REIß
- 2004

We study the problem of estimating the coefficients of a diffusion (X t , t ≥ 0); the estimation is based on discrete data X nn , n = 0, 1,. .. , N. The sampling frequency −1 is constant, and asymptotics are taken as the number N of observations tends to infinity. We prove that the problem of estimating both the diffusion coefficient (the volatility) and… (More)

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