IdentiÞcation of nonlinear stochastic processes via differential neural networks is discussed. A new ”dead-zone” type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis the stability conditions for the identiÞcation error as well as for the neural network weights are established. The adaptive trajectory tracking using the obtained neural network model is r...

A compound Poisson process is considered. We estimate the current position of the stochastic process based on past discrete-time observations (non-linear discrete filtering problem) in Bayesian setting. We obtain bounds for the asymptotic rate of the expected square error of the filter when observations become frequent. The bounds are asymptotically free of process’ parameters. Also, estimation...

For the dimensioning of shared resources, the latency and utilization of the service is a vital design characteristic. The throughput and latency is as important for e.g. network streaming applications as in e.g. (small-scale) distributed embedded systems interacting with physical processes. Calculating latencies of a system involves the analysis of the queue sojourn times. The analysis of queu...

In general, multistage stochastic optimization problems are formulated on the basis of continuous distributions describing the uncertainty. Such “infinite” problems are practically impossible to solve as they are formulated and finite tree approximations of the underlying stochastic processes are used as proxies. In this paper, we demonstrate how one can find guaranteed bounds, i.e. finite tree...

Multistage stochastic programs bring computational complexity which may increase exponentially in real case problems. For this reason approximation techniques which replace the problem by a simpler one and provide lower and upper bounds to the optimal solution are very useful. In this paper we provide monotonic lower and upper bounds for the optimal objective value of a multistage stochastic pr...

We study H(div) preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an H(div) operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the ArnoldFalk-Winther multigrid algorith...

Upper and lower hard bounds of the expected value on stochastic differential equations can be obtained with the help of the mathematical programming and the Dynkin formula, without recourse to Monte Carlo sample paths simulation. In this paper, we show that feasible solutions of those optimization approaches further provide useful additional information. Namely, feasible solutions provide upper...

An important issue for solving multistage stochastic programs consists in the approximate representation of the (multivariate) stochastic input process in the form of a scenario tree. In this paper, forward and backward approaches are developed for generating scenario trees out of an initial fan of individual scenarios. Both approaches are motivated by the recent stability result in [15] for op...

We consider three shortest path problems in directed graphs with random arc lengths. For the first and the second problems, a risk measure is involved. While the first problem consists in finding a path minimizing this risk measure, the second one consists in finding a path minimizing a deterministic cost, while satisfying a constraint on the risk measure. We propose algorithms solving these pr...

Biochemical processes are inherently stochastic, creating molecular fluctuations in otherwise identical cells. Such "noise" is widespread but has proven difficult to analyze because most systems are sparsely characterized at the single cell level and because nonlinear stochastic models are analytically intractable. Here, we exactly relate average abundances, lifetimes, step sizes, and covarianc...