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We provide necessary and sufficient conditions for stochastic invariance of finite dimensional submanifolds with boundary in Hilbert spaces for stochastic partial differential equations driven by Wiener processes and Poisson random measures. ...
We study stationary max-stable processes {n(t): t is an element of R} admitting a representation of the form n(t) = max(i is an element of N) (U-i +Y-i(t)), where Sigma(infinity)(i=1) delta U-i is a Poisson point process on R with intensity e(-u)du, and Y1 ...
We study the dynamics of systems with deterministic trajectories randomly forced by instantaneous discontinuous jumps occurring according to two different compound Poisson processes. One process, with constant frequency, causes instantaneous positive rando ...
Live update is a promising solution to bridge the need to frequently update a software system with the pressing demand for high availability in mission-critical environments. While many research solutions have been proposed over the years, systems that all ...
This work is a study of three interacting particle systems that are modified versions of the contact process. The contact process is a spin system defined on a graph and is commonly taken as a model for the spread of an infection in a population; transmiss ...
Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...
We present a dynamic network loading model that yields queue length distributions, accounts for spillbacks, and maintains a differentiable mapping from the dynamic demand on the dynamic queue lengths. The approach builds upon an existing stationary queuein ...
Motivated by the analog nature of real-world signals, we investigate continuous-time random processes. For this purpose, we consider the stochastic processes that can be whitened by linear transformations and we show that the distribution of their samples ...
Classical peaks over threshold analysis is widely used for statistical modeling of sample extremes, and can be supplemented by a model for the sizes of clusters of exceedances. Under mild conditions a compound Poisson process model allows the estimation of ...
Modern data storage systems are extremely large and consist of several tens or hundreds of nodes. In such systems, node failures are daily events, and safeguarding data from them poses a serious design challenge. The focus of this thesis is on the data rel ...