Search results for " Stochastic differential equations"
showing 10 items of 15 documents
How diffusivity, thermocline and incident light intensity modulate the dynamics of Deep Chlorophyll Maximum in Tyrrhenian Sea
2015
During the last few years theoretical works have shed new light and proposed new hypotheses on the mechanisms which regulate the spatio-temporal behaviour of phytoplankton communities in marine pelagic ecosystems. Despite this, relevant physical and biological issues, such as effects of the time- dependent mixing in the upper layer, competition between groups, and dynamics of non-stationary deep chlorophyll maxima, are still open questions. In this work, we analyze the spatio-temporal behaviour of five phytoplankton populations in a real marine ecosystem by using a one-dimensional reaction-diffusion-taxis model. The study is performed, taking into account the seasonal variations of environm…
Simulation of BSDEs with jumps by Wiener Chaos Expansion
2016
International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.
STOCHASTIC DYNAMICS OF TWO PICOPHYTOPLANKTON POPULATIONS IN A REAL MARINE ECOSYSTEM
2013
A stochastic reaction-diffusion-taxis model is analyzed to get the stationary distribution along water column of two species of picophytoplankton, that is picoeukaryotes and Prochlorococcus. The model is valid for weakly mixed waters, typical of the Mediterranean Sea. External random fluctuations are considered by adding a multiplicative Gaussian noise to the dynamical equation of the nutrient concentration. The statistical tests show that shape and magnitude of the theoretical concentration profile exhibit a good agreement with the experimental findings. Finally, we study the effects of seasonal variations on picophytoplankton groups, including an oscillating term in the auxiliary equation…
Donsker-Type Theorem for BSDEs: Rate of Convergence
2019
In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence. peerReviewed
Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion …
2013
A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for th…
Stochastic models for phytoplankton dynamics in marine ecosystems
2014
In this thesis, the stochastic advection-reaction-diffusion models are analyzed to obtain the vertical stationary spatial distributions of the main groups of picophytoplankton, which account about for 80% of total chlorophyll on average in Mediterranean Sea. In Chapter 1 we give a short presentation of the experimental and phytoplanktonic data collected during different oceanographic surveys in Mediterranean Sea. In Chapter 2 we introduce the deterministic and stochastic approaches (one-population model) adopted to describe the picoeukaryotes dynamics in Sicily Channel. Moreover, numerical results for the biomass concentration are compared with experimental data by using chi-squared goodnes…
Quadratic backward stochastic differential equations
2017
Tässä tutkielmassa analysoimme takaperoisia stokastisia differentiaaliyhtälöitä. Aloitamme esittelemällä stokastiset prosessit, Brownin liikkeen, stokastiset integraalit ja Itôn kaavan. Tämän jälkeen siirrymme tarkastelemaan stokastisia differentiaaliyhtälöitä ja lopulta takaperoisia stokastisia differentiaaliyhtälöitä. Tämän tutkielman pääaiheena on takaperoiset stokastiset differentiaaliyhtälöt kvadraattisilla oletuksilla. Näillä oletuksilla todistamme olemassaoloteoreeman ja tietyt säännöllisyysehdot takaperoisen stokastisen differentiaaliyhtälön ratkaisulle. In this thesis, we analyze backward stochastic differential equations. We begin by introducing stochastic processes, Brownian moti…
Stochastic models for phytoplankton dynamics in Mediterranean Sea
2016
Abstract In this paper, we review some results obtained from three one-dimensional stochastic models, which were used to analyze picophytoplankton dynamics in two sites of the Mediterranean Sea. Firstly, we present a stochastic advection–reaction–diffusion model to describe the vertical spatial distribution of picoeukaryotes in a site of the Sicily Channel. The second model, which is an extended version of the first one, is used to obtain the vertical stationary profiles of two groups of picophytoplankton, i.e. Pelagophytes and Prochlorococcus, in the same marine site as in the previous case. Here, we include intraspecific competition of picophytoplanktonic groups for limiting factors, i.e.…
Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics
2013
In this paper, by using a stochastic reaction-diffusion-taxis model, we analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters. The model includes intraspecific competition of picophytoplankton for light and nutrients. The multiplicative noise sources present in the model account for random fluctuations of environmental variables. Phytoplankton distributions obtained from the model show a good agreement with experimental data sampled in two different sites of the Sicily Channel. The results could be extended to analyze data collected in different sites of the Mediterranean Sea and to devise predictive models for phytoplankton dynam…
Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition
2018
In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed