Intégrales stochastiques par rapport aux martingales locales
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
Motivated by the well-posedness of birth-and-growth processes, a stochastic geometric differential equation and, hence, a stochastic geometric dynamical system are proposed. In fact, a birth-and-growth process can be rigorously modeled as a suitable combination, involving the Minkowski sum and the Aumann integral, of two very general set-valued processes representing nucleation and growth dynamics, respectively. The simplicity of the proposed geometric approach allows to avoid problems of boundary...
In this paper, we introduce the Itô-Henstock integral of an operator-valued stochastic process and formulate a version of Itô's formula.
We consider a stochastic process which solves an equation where and are real matrices and is a fractional Brownian motion with Hurst parameter . The Kolmogorov backward equation for the function is derived and exponential convergence of probability distributions of solutions to the limit measure is established.