Application of renewal theory to call handover counting and dynamic location management in cellular mobile networks

Mobility management in wireless cellular networks is one of the main issues for resource optimization. It is aimed to keep track of Mobile Stations (MSs) in the different Location Areas (LAs) or Registration Areas (RAs) for an efficient call delivery. The optimization issues of these location strategies look for a minimization of the generated signaling traffic. We describe the three basic strategies for location management: distance-based, time-based and movement-based, and their corresponding optimization cost. We emphasize that counting the number of wireless cell crossings or handovers occurring in the call duration time or during inter-call times is a fundamental issue for mobility management analysis. We present the main approaches in the literature to deal with these problems with a special emphasis to renewal theory to model the probabilistic structure of these optimization problems.Applied probability Wireless networks Location management Handovers

Transformations of Telegraph Processes and Their Financial Applications

In this paper, we consider non-linear transformations of classical telegraph process. The main results consist of deriving a general partial differential Equation (PDE) for the probability density (pdf) of the transformed telegraph process, and then presenting the limiting PDE under Kac’s conditions, which may be interpreted as the equation for a diffusion process on a circle. This general case includes, for example, classical cases, such as limiting diffusion and geometric Brownian motion under some specifications of non-linear transformations (i.e., linear, exponential, etc.). We also give three applications of non-linear transformed telegraph process in finance: (1) application of classical telegraph process in the case of balance, (2) application of classical telegraph process in the case of dis-balance, and (3) application of asymmetric telegraph process. For these three cases, we present European call and put option prices. The novelty of the paper consists of new results for non-linear transformed classical telegraph process, new models for stock prices based on transformed telegraph process, and new applications of these models to option pricing

Asymptotic Estimation of Two Telegraph Particle Collisions and Spread Options Valuations

In this paper, we study collisions of two telegraph particles on a line that are described by telegraph processes between collisions. We obtain an asymptotic estimation of the number of collisions under Kac’s condition for the cases where the direction-switching processes have the same parameters and different parameters. We also consider the application of these results to evaluate Margrabe’s spread option for two assets of spot prices modeled by two telegraph processes