Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion Export

@article{citeulike:3955138, abstract = {We construct a stochastic model for coagulation-fragmen- tation processes and analyze its convergence properties toward the solution of the deterministic coagulation-fragmentation equations with diffusion. The model can be described as follows: we approximate a domain \&b.Omega; by cubic cells of size \&b.epsi;, and consider particles of sizes 1,2,, <i>k</i>,, <i>N</i>. Inside each cell can occur one of the folllowing reactions: a particle of size <i>i</i> can collide with a particle of size <i>j</i> and form a new particle of size <i>i</i> + <i>j</i>, or a particle of size <i>i</i> can split into a particle of size <i>j</i> and a particle of size <i>i</i> - <i>j</i>. The diffusion is approximated by random walks performed between the cells by the <i>k</i>-fold clusters, <i>k</i> = 1, 2, , <i>N</i>. Under the hypothesis of bounded coagulation coefficients, we prove a result of convergence in probability toward the solution of the deterministic equations, by using the martingale characterization of the Markov process restated in a form corresponding to the mild semigroup formulation of the dynamics.}, author = {Guia\c{s}, Flavius}, citeulike-article-id = {3955138}, citeulike-linkout-0 = {http://dx.doi.org/10.1081/SAP-100001188}, doi = {10.1081/SAP-100001188}, journal = {Stochastic Analysis and Applications}, keywords = {cfdiffusion, coagulation, diffusion, existence, fragmentation, stochastic}, number = {2}, pages = {245--278}, posted-at = {2009-01-26 18:25:54}, priority = {2}, publisher = {Taylor \& Francis}, title = {Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion}, url = {http://dx.doi.org/10.1081/SAP-100001188}, volume = {19}, year = {2001} }

TY - JOUR ID - citeulike:3955138 L3 - citeulike-article-id:3955138 N2 - We construct a stochastic model for coagulation-fragmen- tation processes and analyze its convergence properties toward the solution of the deterministic coagulation-fragmentation equations with diffusion. The model can be described as follows: we approximate a domain &b.Omega; by cubic cells of size &b.epsi;, and consider particles of sizes 1,2,, <i>k</i>,, <i>N</i>. Inside each cell can occur one of the folllowing reactions: a particle of size <i>i</i> can collide with a particle of size <i>j</i> and form a new particle of size <i>i</i> + <i>j</i>, or a particle of size <i>i</i> can split into a particle of size <i>j</i> and a particle of size <i>i</i> - <i>j</i>. The diffusion is approximated by random walks performed between the cells by the <i>k</i>-fold clusters, <i>k</i> = 1, 2, , <i>N</i>. Under the hypothesis of bounded coagulation coefficients, we prove a result of convergence in probability toward the solution of the deterministic equations, by using the martingale characterization of the Markov process restated in a form corresponding to the mild semigroup formulation of the dynamics. IS - 2 JF - Stochastic Analysis and Applications EP - 278 TI - Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion PB - Taylor & Francis VL - 19 SP - 245 KW - cfdiffusion KW - coagulation KW - diffusion KW - existence KW - fragmentation KW - stochastic AU - Guiaş, Flavius PY - 2001/// UR - http://dx.doi.org/10.1081/SAP-100001188 ER -