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The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…
The first part of the paper studies the expression for, and the properties of, the logarithm map on an orthant space, which is a simple stratified space, with the aim of analysing Frechet means of probability measures on such a space. In…
Virtually all practical settings where preemptive scheduling is employed are susceptible to preemption overhead, and accounting for these overheads is necessary to make informed scheduling design decisions. However, preemption overhead is…
This work focuses on a class of semi-linear functional stochastic partial differential equations with Markovian switching, in which the switching component may have finite or countably infinite states. The well-posedness of the underlying…
In this paper, we show that the concept of sigma-convergence associated to stochastic processes can tackle the homogenization of stochastic partial differential equations. In this regard, the homogenization problem for a stochastic…
We prove a robust super-hedging duality result for path-dependent options on assets with jumps, in a continuous time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some…
Partial differential equation-based numerical solution frameworks for initial and boundary value problems have attained a high degree of complexity. Applied to a wide range of physics with the ultimate goal of enabling engineering…
We propose a new Statistical Complexity Measure (SCM) to qualify edge maps without Ground Truth (GT) knowledge. The measure is the product of two indices, an \emph{Equilibrium} index $\mathcal{E}$ obtained by projecting the edge map into a…
Contrary to previous approaches bringing together algebraic geometry and signatures of paths, we introduce a Zariski topology on the space of paths itself, and study path varieties consisting of all paths whose iterated-integrals signature…
Co-flows model a modern scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. A stochastic co-flow task contains a set of parallel flows with randomly distributed sizes. Further, many…
Quantum walks are promising tools based on classical random walks, with plenty of applications such as many variants of optimization. Here we introduce the semiclassical walks in discrete time, which are algorithms that combines classical…
Consider a stochastic process $\{X(t)\}$ on a finite state space $ {\sf X}=\{1,\dots, d\}$. It is conditionally Markov, given a real-valued `input process' $\{\zeta(t)\}$. This is assumed to be small, which is modeled through the scaling,…
Queueing systems are widely applicable stochastic models with use cases in communication networks, healthcare, service systems, etc. Although their optimal control has been extensively studied, most existing approaches assume perfect…
We extend stochastic network optimization theory to treat networks with arbitrary sample paths for arrivals, channels, and mobility. The network can experience unexpected link or node failures, traffic bursts, and topology changes, and…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
Estimating time-resolved velocity and pressure fields from Particle Image Velocimetry (PIV) remains challenging due to its limited temporal resolution in many applications. Data-driven approaches that combine snapshot PIV with…
In this paper, we establish the partial correlation graph for multivariate continuous-time stochastic processes, assuming only that the underlying process is stationary and mean-square continuous with expectation zero and spectral density…
The critical path of a group of tasks is an important measure that is commonly used to guide task allocation and scheduling on parallel computers. The critical path is the longest chain of dependencies in an acyclic task dependence graph. A…
We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving…