A stochastic differential equation with a unique (up to indistinguishability) but not strong solution
A stochastic extension of R. Thomas regulatory network modelling
In this paper we present the extension of the kinetic logic proposed by René Thomas for analysis of genetic regulatory gene networks. We consider the case with a Gaussian noise added to the regulation function and propose a method of analyzing the resulting model with a discrete time Markov model.
A stochastic fixed point equation for weighted minima and maxima
Given any finite or countable collection of real numbers Tj, j∈J, we find all solutions Fto the stochastic fixed point equation whereW and the Wj, j∈J, are independent real-valued random variables with distribution Fand means equality in distribution. The bulk of the necessary analysis is spent on the case when |J|≥2 and all Tj are (strictly) positive. Nontrivial solutions are then concentrated on either the positive or negative half line. In the most interesting (and difficult) situation T...
A stochastic fixed point equation related to weighted branching with deterministic weights.
A stochastic functional equation. (Short Communication).
A stochastic Gronwall inequality and its applications.
A stochastic inventory model with perishable and aging items.
A stochastic inventory model with stock dependent demand items.
A stochastic lagrangian proof of global existence of the Navier-Stokes equations for flows with small Reynolds number
A stochastic min-driven coalescence process and its hydrodynamical limit
A stochastic system of particles is considered in which the sizes of the particles increase by successive binary mergers with the constraint that each coagulation event involves a particle with minimal size. Convergence of a suitably renormalized version of this process to a deterministic hydrodynamical limit is shown and the time evolution of the minimal size is studied for both deterministic and stochastic models.
A stochastic model for the financial market with discontinuous prices.
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 Multiplicative Model in Assessment of Training Programs
A stochastic Paris-Erdogan model for fatigue crack growth using two-state 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 stochastic two-point boundary value problem.