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)
We introduce and analyze numerical methods for the treatment of inverse problems , based on an adaptive wavelet Galerkin discretization. These methods combine the theoretical advantages of the wavelet-vaguelette decomposition (WVD) in terms of optimally adapting to the unknown smoothness of the solution, together with the numerical simplicity of Galerkin… (More)
We study the problem of estimating the coefficients of a diffu-−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 the drift in a nonparametric setting is ill-posed: the minimax rates of convergence for Sobolev constraints and… (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)
Hawkes processes are used for modeling tick-by-tick variations of a single or of a pair of asset prices. For each asset, two counting processes (with stochastic intensities) are associated respectively with the positive and negative jumps of the price. We show that, by coupling these two intensities, one can reproduce high-frequency mean reversion structure… (More)
Multifractal analysis of multiplicative random cascades is revis-ited within the framework of mixed asymptotics. In this new framework , statistics are estimated over a sample which size increases as the resolution scale (or the sampling period) becomes finer. This allows one to continuously interpolate between the situation where one studies a single… (More)
In this note, we present results on the behavior for the partition function of multiplicative cascades in the case where the total time of observation is large, compared to the scale of decay for the correlation of the cascade process.