This paper addresses ergodicity and throughput bounds characterizations for a subclass of timed and stochas-tic Petri nets, interleaving qualitative and quantitative theories. The considered nets represent an extension of the well known subclass of marked graphs, deened as having a unique consistent ring count vector, independently of the stochastic interpretation of the net model. In particula...

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can be applied to obtain upper bounds for the growth of bounded sets under the action of a stochastic flow.

In this note we develop a framework for computing upper and lower bounds of an exponential form for a class of stochastic recursive equations with uniformly recurrent Markov modulated inputs. These bounds generalize Kingman's bounds for queues with renewal inputs.

Recently some stochastic (probabilistic) extensions of the deterministic network calculus have been developed, mainly for exploiting the statistical multiplexing of flows aggregated in packet based communication networks. This exploitation could result ”better” stochastic performance bounds than those bounds provided by the inherently worst case analysis of the deterministic network calculus. T...

Emerging techniques now allow for precise quantification of distributions of biological molecules in single cells. These rapidly advancing experimental methods have created a need for more rigorous and efficient modeling tools. Here, we derive new bounds on the likelihood that observations of single-cell, single-molecule responses come from a discrete stochastic model, posed in the form of the ...

It has been suggested that stochastic flows might be used to model the spread of passive tracers in a turbulent fluid. We define a stochastic flow by the equations φ0 x = x dφt x = F dt φt x where F t x is a field of semimartingales on x ∈ d for d ≥ 2 whose local characteristics are bounded and Lipschitz. The particles are points in a bounded set , and we ask how far the substance has spread in...

Stochastic-approximation gradient methods are attractive for large-scale convex optimization because they offer inexpensive iterations. They are especially popular in data-fitting and machine-learning applications where the data arrives in a continuous stream, or it is necessary to minimize large sums of functions. It is known that by appropriately decreasing the variance of the error at each i...

This results in this paper have been merged with the result in arXiv:1003.0167. The authors would like to withdraw this version. Please see arXiv:1008.5356 for the merged version.