In the present paper, a class of stochastic Runge–Kutta methods containing the second order stochastic Runge–Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2...

We consider scalar stochastic differential equations of the formdXt=μ(Xt)dt+σ(Xt)dBt,X0=x0,where B is a standard Brownian motion. Suppose that the coefficients are such that the solution X possesses the (a, b)-invariance property for some interval (a,b)⊂R:Xt∈(a,b) for all t≥0 if...

The present analysis is an application of the continuous time replicator dynamic to economics. Three types of problems are considered under conditions of a normalized constraint and non-negative constrains. The story of the following models is as follows. There are three or more corporations in...

This paper deals with numerical solution of two-dimensional and three-dimensional steady and unsteady laminar incompressible flows for Newtonian and non-Newtonian shear thickening fluids flow through a branching channel. The mathematical model used in this work is the generalized system of...

This paper deals with the numerical solution of Newtonian and non-Newtonian flows with biomedical applications. The flows are supposed to be laminar, viscous, incompressible and steady or unsteady with prescribed pressure variation at the outlet. The model used for non-Newtonian fluids is a...

We propose two new positive weak second-order approximations for the CIR equation dXt=(a−bXt)dt+σXtdBt based on splitting, at each step, the equation into the deterministic part dXt=(a−bXt)dt, which is solved exactly, and the stochastic part dXt=σXtdBt, which is approximated in...

Understanding the behaviour of market prices is not simple. Stock market prices tend to have complicated distributions with strong skewness and fat tails. One important step in forecasting tomorrow’s price is to estimate the volatility, i.e. how much tomorrow’s price is expected to differ...

An efficient methodology of estimation of parameters in the diffusion coefficient of the stochastic differential equation (SDE) is presented in this work. The methodology is based on the concept of quadratic variation of a stochastic process and on some classical numerical tools such as spline...

We consider a stochastic model of the two-dimensional chemostat as a diffusion process for the concentration of substrate and the concentration of biomass. The model allows for the washout phenomenon: the disappearance of the biomass inside the chemostat. We establish the Fokker–Planck...

The phenomenon of ‘synchronization’ of physical diffusion is widely discussed in the physical literature. In this paper, we give a simple rigorous proof of the synchronization for a one-dimensional diffusion including the one-dimensional counterpart of a physical diffusion described by a...