Search results for " Stochastic processes"
showing 10 items of 35 documents
Diversifying selection on MHC class I in the house sparrow (Passer domesticus).
2009
10 pages; International audience; Genes of the major histocompatibility complex (MHC) are the most polymorphic loci known in vertebrates. Two main hypotheses have been put forward to explain the maintenance of MHC diversity: pathogen-mediated selection and MHC-based mate choice. Host-parasite interactions can maintain MHC diversity via frequency-dependent selection, heterozygote advantage, and diversifying selection (spatially and/or temporally heterogeneous selection). In this study, we wished to investigate the nature of selection acting on the MHC class I across spatially structured populations of house sparrows (Passer domesticus) in France. To infer the nature of the selection, we comp…
The role of noise on the steady state distributions of phytoplankton populations
2016
The spatio-temporal behaviour of total chlorophyll concentration is investigated in the middle of the Tyrrhenian Sea by using a stochastic approach. The study is based on a reaction-diffusion-taxis model, which is used to analyse the dynamics of five phytoplankton groups, responsible for about 80% of the total chlorophyll a inside the euphotic zone of the water column. The analysis is performed by considering: (i) the intraspecific competition of the phytoplanktonic groups for limiting factors, i.e. light intensity and nutrient concentration, (ii) the seasonal changes of environmental variables, and (iii) the random fluctuations of the components of the velocity field and temperature. Speci…
Bayesian hierarchical models for analysing the spatial distribution of bioclimatic indices
2017
A methodological approach for modelling the spatial distribution of bioclimatic indices is proposed in this paper. The value of the bioclimatic index is modelled with a hierarchical Bayesian model that incorporates both structured and unstructured random effects. Selection of prior distributions is also discussed in order to better incorporate any possible prior knowledge about the parameters that could refer to the particular characteristics of bioclimatic indices. MCMC methods and distributed programming are used to obtain an approximation of the posterior distribution of the parameters and also the posterior predictive distribution of the indices. One main outcome of the proposal is the …
Market reaction to a bid-ask spread change: a power-law relaxation dynamics.
2009
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of price…
Quadratic variation of martingales in Riesz spaces
2014
We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)
Relations between structure and estimators in networks of dynamical systems
2011
The article main focus is on the identification of a graphical model from time series data associated with different interconnected entities. The time series are modeled as realizations of stochastic processes (representing nodes of a graph) linked together via transfer functions (representing the edges of the graph). Both the cases of non-causal and causal links are considered. By using only the measurements of the node outputs and without assuming any prior knowledge of the network topology, a method is provided to estimate the graph connectivity. In particular, it is proven that the method determines links to be present only between a node and its “kins”, where kins of a node consist of …
Tick size and price diffusion
2010
A tick size is the smallest increment of a security price. It is clear that at the shortest time scale on which individual orders are placed the tick size has a major role which affects where limit orders can be placed, the bid-ask spread, etc. This is the realm of market microstructure and there is a vast literature on the role of tick size on market microstructure. However, tick size can also affect price properties at longer time scales, and relatively less is known about the effect of tick size on the statistical properties of prices. The present paper is divided in two parts. In the first we review the effect of tick size change on the market microstructure and the diffusion properties…
How markets slowly digest changes in supply and demand
2008
In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly incorporated into prices. Because revealed market liquidity is extremely low, large orders to buy or sell can only be traded incrementally, over periods of time as long as months. As a result order flow is a highly persistent long-memory process. Maintaining compatibility with market efficiency has profound consequences on price formation, on the dynamics of liquidity, and on the nature of impact. We review a body of theory that makes detailed quantitative pr…
Stability in a System subject to Noise with Regulated Periodicity
2011
The stability of a simple dynamical system subject to multiplicative one-side pulse noise with hidden periodicity is investigated both analytically and numerically. The stability analysis is based on the exact result for the characteristic functional of the renewal pulse process. The influence of the memory effects on the stability condition is analyzed for two cases: (i) the dead-time-distorted poissonian process, and (ii) the renewal process with Pareto distribution. We show that, for fixed noise intensity, the system can be stable when the noise is characterized by high periodicity and unstable at low periodicity.
Two competing species in super-diffusive dynamical regimes
2010
The dynamics of two competing species within the framework of the generalized Lotka-Volterra equations, in the presence of multiplicative alpha-stable Lévy noise sources and a random time dependent interaction parameter, is studied. The species dynamics is characterized by two different dynamical regimes, exclusion of one species and coexistence of both, depending on the values of the interaction parameter, which obeys a Langevin equation with a periodically fluctuating bistable potential and an additive alpha-stable Lévy noise. The stochastic resonance phenomenon is analyzed for noise sources asymmetrically distributed. Finally, the effects of statistical dependence between multiplicative …