Asymptotic behaviour of point processes with Markov-dependent intervals

This splitting techniques for MARKOV chains developed by NUMMELIN (1978a) and ATHREYA and NEY (1978b) are used to derive an imbedded renewal process in WOLD's point process with MARKOV-correlated intervals. This leads to a simple proof of renewal theorems for such processes. In particular, a key renewal theorem is proved, from which analogues to both BLACKWELL's and BREIMAN's forms of the renewal theorem can be deduced.

Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

On the Milito-Cruz adaptive control scheme for Markov chains

Milito and Cruz have introduced a novel adaptive control scheme for finite Markov chains when a finite parametrized family of possible transition matrices is available. The scheme involves the minimization of a composite functional of the observed history of the process incorporating both control and estimation aspects. We prove the a.s. optimality of a similar scheme when the state space is countable and the parameter space a compact subset ofR.

Risk Minimizing Option Pricing for a Class of Exotic Options in a Markov-Modulated Market

We address risk minimizing option pricing in a regime switching market where the floating interest rate depends on a finite state Markov process. The growth rate and the volatility of the stock also depend on the Markov process. Using the minimal martingale measure, we show that the locally risk minimizing prices for certain exotic options satisfy a system of Black-Scholes partial differential equations with appropriate boundary conditions. We find the corresponding hedging strategies and the residual risk. We develop suitable numerical methods to compute option prices.

Structured systems methodology for evaluation of random interruptions in continuous process type manufacturing systems

A structured systems methodology was developed to analyse the problems of production interruptions occurring at random intervals in continuous process type manufacturing systems. At a macro level the methodology focuses on identifying suitable investment policies to reduce interruptions of a total manufacturing system that is a combination of several process plants. An interruption-tree-based simulation model was developed for macroanalysis. At a micro level the methodology focuses on finding the effects of alternative configurations of individual process plants on the overall system performance. A Markov simulation model was developed for microlevel analysis. The methodology was tested with an industry-specific application.

Residence time distribution for a class of Gaussian Markov processes

We study the distribution of residence time or equivalently that of "mean magnetization" for a family of Gaussian Markov processes indexed by a positive parameter alpha. The persistence exponent for these processes is simply given by theta=alpha but the residence time distribution is nontrivial. The shape of this distribution undergoes a qualitative change as theta increases, indicating a sharp change in the ergodic properties of the process. We develop two alternate methods to calculate exactly but recursively the moments of the distribution for arbitrary alpha. For some special values of alpha, we obtain closed form expressions of the distribution function. [S1063-651X(99)03306-1].

Performance analysis of UDP with energy efficient link layer on Markov fading channels

In this paper, we analyze the throughput and energy efficiency performance of user datagram protocol (UDP) using linear, binary exponential, and geometric backoff algorithms at the link layer (LL) on point-to-point wireless fading links. Using a first-order Markov chain representation of the packet success/failure process on fading channels, we derive analytical expressions for throughput and energy efficiency of UDP/LL with and without LL backoff. The analytical results are verified through simulations. We also evaluate the mean delay and delay variation of voice packets and energy efficiency performance over a wireless link that uses UDP for transport of voice packets and the proposed backoff algorithms at the LL. We show that the proposed LL backoff algorithms achieve energy efficiency improvement of the order of 2-3 dB compared to LL with no backoff, without compromising much on the throughput and delay performance at the UDP layer. Such energy savings through protocol means will improve the battery life in wireless mobile terminals.

Markov chain modeling of evolution of strains in reinforced concrete flexural beams

From the analysis of experimentally observed variations in surface strains with loading in reinforced concrete beams, it is noted that there is a need to consider the evolution of strains (with loading) as a stochastic process. Use of Markov Chains for modeling stochastic evolution of strains with loading in reinforced concrete flexural beams is studied in this paper. A simple, yet practically useful, bi-level homogeneous Gaussian Markov Chain (BLHGMC) model is proposed for determining the state of strain in reinforced concrete beams. The BLHGMC model will be useful for predicting behavior/response of reinforced concrete beams leading to more rational design.

LANDSCAPE DYNAMICS MODELING THROUGH INTEGRATED MARKOV, FUZZY-AHP AND CELLULAR AUTOMATA

Multi temporal land use information were derived using two decades remote sensing data and simulated for 2012 and 2020 with Cellular Automata (CA) considering scenarios, change probabilities (through Markov chain) and Multi Criteria Evaluation (MCE). Agents and constraints were considered for modeling the urbanization process. Agents were nornmlized through fiizzyfication and priority weights were assigned through Analytical Hierarchical Process (AHP) pairwise comparison for each factor (in MCE) to derive behavior-oriented rules of transition for each land use class. Simulation shows a good agreement with the classified data. Fuzzy and AHP helped in analyzing the effects of agents of growth clearly and CA-Markov proved as a powerful tool in modelling and helped in capturing and visualizing the spatiotemporal patterns of urbanization. This provided rapid land evaluation framework with the essential insights of the urban trajectory for effective sustainable city planning.

Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.