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.
A stochastic version of Fan's best approximation theorem.
A stopping time problem on the positive integers
A strong invariance principle for negatively associated random fields
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite th moment and the covariance coefficient exponentially decreases to . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
A strong invariance theorem for the tail empirical process
A strong law of large numbers for harmonizable isotropic random fields.
A strong law of large numbers for identically distributed vector lattice-valued random variables
A strong limit theorem for functions of continuous random variables and an extension of the Shannon-McMillan theorem.
A strong limit theorem for weighted sums of sequences of negatively dependent random variables.
A strong mixing condition for second-order stationary random fields
Let be a second-order stationary random field on Z². Let ℳ(L) be the linear span of , and ℳ(RN) the linear span of . Spectral criteria are given for the condition , where is the cosine of the angle between ℳ(L) and .
A Stroock formula for a certain class of Lévy processes and applications to finance.
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A study of the dynamic of influence through differential equations∗
The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...
A Subsequence Principle in Probability Theory. II. The Law of the Iterated Logarithm.