A stochastic fixed point equation related to weighted branching with deterministic weights.
A stochastic inventory model with perishable and aging items.
A stochastic inventory model with stock dependent demand items.
A stochastic model of symbiosis
We consider a system of stochastic differential equations which models the dynamics of two populations living in symbiosis. We prove the existence, uniqueness and positivity of solutions. We analyse the long-time behaviour of both trajectories and distributions of solutions. We give a biological interpretation of the model.
A stochastic phase-field model determined from molecular dynamics
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...
A stochastic scheme for constructing solutions of the Schrödinger equations
A stochastic scheme of approximation for ordinary differential equations.
A stochastic symbiosis model with degenerate diffusion process
We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.
A stochastic two species competition model: nonequilibrium fluctuation and stability.
A sufficient condition for the Carasso-Kato theorem.
A sufficient condition for the Carasso-Kato theorem (Erratum).
A superprocess involving both branching and coalescing
A super-stable motion with infinite mean branching
A survey of random processes with reinforcement.
A survey of the literature associated with the bisexual Galton-Watson branching process.
A symbolic calculus and a parametrix construction for pseudodifferential operators with non-smooth negative definite symbols.
A Theorem on Convergence to a Lévy Process.
A trivariate law for certain processes related to perturbed brownian motions
A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.
A unified approach to several inequalities for gaussian and diffusion measures