We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov’s approach to foreign exchange markets under transaction costs. The financial market is modelled by a d × d matrix-valued stochastic process (Σt)t=0 specifying the mutual bid and ask prices between d assets. We introduce the notion of “robust no arbitrage”, which is a version of the no arbitrage concept, ro...

The problem of Window Flow Controlled (WFC) systems has been analysed successfully in Deterministic Network Calculus (DNC). While many results of DNC have been carried over to its stochastic extension, the problem of WFC systems has not been solved so far. This paper presents the first approach to analyse WFC in the context of Stochastic Network Calculus (SNC) for a general service inside the f...

Stochastic behavior—the probabilistic evolution of a system in time—is essential to modeling the complexity of real-world systems. It enables realistic performance modeling, quality-of-service guarantees, and especially simulations for biological systems. Languages like the stochastic pi calculus have emerged as effective tools to describe and reason about systems exhibiting stochastic behavior...

A key challenge of ubiquitous computing environments, which feature massively distributed systems containing a large number of contexts and services, is how to manage the relations between context and service. Some researchers use rules to describe these relations, while other researchers propose stochastic methods to model them. However, both approaches have serious problems cannot be solved b...

Many communication networks such as wireless networks only provide stochastic service guarantees. For analyzing stochastic service guarantees, research effort has been made in the past few years to develop stochastic network calculus, a probabilistic version of (min, +) deterministic network calculus. However, many challenges have made the development difficult. Some of them are closely related...

Many studies focus on inventory systems to analyze different real-world situations. This paper considers a two-echelon supply chain that includes one warehouse and one retailer with stochastic demand and an up-to-level policy. The retailer’s lead time includes the transportation time from the warehouse to the retailer that is unknown to the retailer. On the other hand, the warehouse is unaware ...

The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic dynamic systems are given, and examples of evaluation of the exponent for systems with matrices of particular types are presented. A method which allow one to get ...

a memory control for t-s fuzzy discrete-time systems with sto- chastic input delay is proposed in this paper. dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis- tribution. a new state space model of the discrete-time t-s fuzzy system is derived by introducing some stocha...

In this paper, a novel scenario-based two-level inventory control model with a limited budget is formulated. The demand during the selling period is considered to follow a uniform probability distribution. In addition, it is assumed that there will be some customers who are willing to wait for their demands to be satisfied; thus a service level is considered for these customers. The aim is to f...

Network Calculus Analysis of Feedback Systems with Random Service Alireza Shekaramiz Master of Applied Science Graduate Department of Electrical and Computer Engineering University of Toronto 2015 Feedback systems are deployed in many network related applications and various analytical approaches have tried to evaluate the performance of these systems. Network calculus is one such approach that...