We study the two-dimensional fractional Brownian motion with Hurst parameter H > 1 2. In particular, we show, using stochastic calculus , that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

We consider a new class of optimization problems involving stochastic dominance constraints of second order. We develop a new splitting approach to these models, optimality conditions and duality theory. These results are used to construct special decomposition methods.

Based on the wavelet-defined multiscale random noise proposed in [2], a multiscale version of the stochastic quantization procedure is considered. A new type of the commutation relations emerging from the multiscale decomposition of the operator-valued fields is derived.

This paper discusses hybrid probabilistic and fuzzy set approaches to propagating randomness and imprecision in risk assessment and fuzzy time series models. Stochastic and Computational Intelligence methods, such as Probability bounds analysis, Fuzzy -levels analysis, Fuzzy random vectors, Wavelets decomposition and Wavelets Networks are combined to capture different kinds of uncertainty. The...

This document shows how to model two-stage stochastic linear programming problems in a GAMS environment. We will demonstrate using a small example, how GAMS can be used to formulate and solve this model as a large LP or using specialized stochastic solvers such as OSL-SE and DECIS. Finally a tailored implementation of the Benders Decomposition algorithm written in GAMS is used to solve the model.

We consider two-stage stochastic programming problems with integer recourse. The L-shaped method of stochastic linear programming is generalized to these problems by using generalized Benders decomposition. Nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques. Finite convergence of...

We introduce stochastic integer programs with dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed-integer linear programming equivalents to the dominance constrained stochastic programs are id...

By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total energy difference into the work and the heat for each trajectory, and derive a formula to calculate the heat from experimental data on the dynamics. We apply our formulation and results to a Langevin...

We are interested in the persistence in mean and extinction for a stochastic competitive Gilpin-Ayala system with regime switching. Based on the stochastic LaSalle theorem and the space-decomposition method, we derive generalized sufficient criteria on persistence in mean and extinction. By constructing a novel Lyapunov function we establish sufficient criteria on partial persistence in mean an...

In this talk we discuss the use of domain decomposition parallel iterative solvers for highly heterogeneous problems of flow in porous media, in both the deterministic and (Monte-Carlo simulated) stochastic cases. We are particularly interested in the case of highly unstructured coefficient variation where standard periodic or stochastic homogenisation theory is not applicable, and where there ...