Basics of Stochastic Analysis c © 2003

Control and Financial Engineering

The paper provides a review of the basics of financial engineering, with a few examples. We emphasize connections with control theory in a broad sense rather than with stochastic control theory in particular, and the reader is not assumed to be versed in stochastic processes. After a discussion of the main methods of financial risk management, a state-space framework for modeling financial mark...

Diffusion Processes on Manifolds

This is an informal introduction to stochastic analysis on both Riemanian and Lorentzian manifolds. We review the basics underlying the construction of diffusions on manifolds, highlighting the important differences between the Riemanian and Lorentzian cases. We also discuss a few recent applications which range from biophysics to cosmology.

Explanation of Theoretical Basics of Analysis of the World Order

Shrinkage Curve: Experimental Study and Modelling

In order to study the shrinkage process of clayey soil, we perform a modified laboratory test allowing to measure simultaneously and continuously the vertical displacement and the weight of natural state specimen. The experiment was conducted on undisturbed clayey specimen. Using the experimental results, and on the basis of the existing relation between the soil water content and its structura...

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...