**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2740

# Search results for: Stochastic models

##### 2740 A Computational Stochastic Modeling Formalism for Biological Networks

**Authors:**
Werner Sandmann,
Verena Wolf

**Abstract:**

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

**Keywords:**
Computational Modeling,
Biological Networks,
Stochastic Models,
Markov Chains,
Transition Class Models.

##### 2739 Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics

**Authors:**
Teh Raihana Nazirah Roslan,
Siti Zulaiha Ibrahim,
Sharmila Karim

**Abstract:**

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

**Keywords:**
Cox-Ingersoll-Ross model,
equity warrants,
Heston model,
hybrid models,
stochastic.

##### 2738 TS Fuzzy Controller to Stochastic Systems

**Authors:**
Joabe Silva,
Ginalber Serra

**Abstract:**

**Keywords:**
Fuzzy Systems; Robust Stability,
Stochastic Control,
Stochastic Process

##### 2737 Stochastic Learning Algorithms for Modeling Human Category Learning

**Authors:**
Toshihiko Matsuka,
James E. Corter

**Abstract:**

**Keywords:**
category learning,
cognitive modeling,
radial basis
function,
stochastic optimization.

##### 2736 Comparative Analysis of the Stochastic and Parsimonious Interest Rates Models on Croatian Government Market

**Authors:**
Zdravka Aljinović,
Branka Marasović,
Blanka Škrabić

**Abstract:**

**Keywords:**
the term structure of interest rates,
Vasicek model,
Nelson-Siegel model,
Croatian Government market.

##### 2735 Calculation of Reorder Point Level under Stochastic Parameters: A Case Study in Healthcare Area

**Authors:**
Serap Akcan,
Ali Kokangul

**Abstract:**

**Keywords:**
Inventory control system,
reorder point level,
stochastic demand,
stochastic lead time

##### 2734 Wind Power Forecast Error Simulation Model

**Authors:**
Josip Vasilj,
Petar Sarajcev,
Damir Jakus

**Abstract:**

One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

**Keywords:**
Wind power,
Uncertainty,
Stochastic process,
Monte
Carlo simulation.

##### 2733 Non-Stationary Stochastic Optimization of an Oscillating Water Column

**Authors:**
María L. Jalón,
Feargal Brennan

**Abstract:**

**Keywords:**
Non-stationary stochastic optimization,
oscillating
water column,
temporal variability,
wave energy.

##### 2732 Dynamic Slope Scaling Procedure for Stochastic Integer Programming Problem

**Authors:**
Takayuki Shiina

**Abstract:**

**Keywords:**
stochastic programming problem with recourse,
simple
integer recourse,
dynamic slope scaling procedure

##### 2731 Stochastic Estimation of Cavity Flowfield

**Authors:**
Yin Yin Pey,
Leok Poh Chua,
Wei Long Siauw

**Abstract:**

**Keywords:**
Open cavity,
Particle Image Velocimetry,
Stochastic
estimation,
Turbulent kinetic energy.

##### 2730 Stochastic Programming Model for Power Generation

**Authors:**
Takayuki Shiina

**Abstract:**

**Keywords:**
electric power capacity expansion problem,
integerprogramming,
L-shaped method,
stochastic programming

##### 2729 Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models

**Authors:**
Maria C. Mariani,
Md Al Masum Bhuiyan,
Osei K. Tweneboah,
Hector G. Huizar

**Abstract:**

**Keywords:**
Augmented Dickey Fuller Test,
geophysical time
series,
maximum likelihood estimation,
stochastic volatility model.

##### 2728 The Martingale Options Price Valuation for European Puts Using Stochastic Differential Equation Models

**Authors:**
H. C. Chinwenyi,
H. D. Ibrahim,
F. A. Ahmed

**Abstract:**

In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

**Keywords:**
Equivalent Martingale Measure,
European Put Option,
Girsanov Theorem,
Martingales,
Monte Carlo method,
option price valuation,
option price valuation formula.

##### 2727 The Proof of Analogous Results for Martingales and Partial Differential Equations Options Price Valuation Formulas Using Stochastic Differential Equation Models in Finance

**Authors:**
H. D. Ibrahim,
H. C. Chinwenyi,
A. H. Usman

**Abstract:**

Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

**Keywords:**
Option price valuation,
Martingales,
Partial Differential Equations,
PDEs,
Equivalent Martingale Measure,
Girsanov Theorem,
Feyman-Kac Theorem,
European Put Option.

##### 2726 Stochastic Scheduling to Minimize Expected Lateness in Multiple Identical Machines

**Authors:**
Ghulam Zakria,
Zailin Guan ,
Yasser Riaz Awan,
Wan Lizhi

**Abstract:**

**Keywords:**
Quantity Production Flow Shop,
LPT Scheduling,
Stochastic Scheduling,
Maximum Lateness,
Random Due Dates

##### 2725 Comparison of Reliability Systems Based Uncertainty

**Authors:**
A. Aissani,
H. Benaoudia

**Abstract:**

**Keywords:**
Uncertainty,
Stochastic comparison,
Reliability,
serie's system,
imperfect repair.

##### 2724 On Diffusion Approximation of Discrete Markov Dynamical Systems

**Authors:**
Jevgenijs Carkovs

**Abstract:**

**Keywords:**
Markov dynamical system,
diffusion approximation,
equilibrium stochastic stability.

##### 2723 The Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching

**Authors:**
Dezhi Liu Guiyuan Yang Wei Zhang

**Abstract:**

**Keywords:**
Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

##### 2722 Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps

**Authors:**
Dezhi Liu

**Abstract:**

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

**Keywords:**
Impulsive,
stochastic,
delay,
Markovian switching,
Poisson jumps,
mean square stability.

##### 2721 Application of Stochastic Models to Annual Extreme Streamflow Data

**Authors:**
Karim Hamidi Machekposhti,
Hossein Sedghi

**Abstract:**

**Keywords:**
Stochastic models,
ARIMA,
extreme streamflow,
Karkheh River.

##### 2720 Segmentation of Noisy Digital Images with Stochastic Gradient Kernel

**Authors:**
Abhishek Neogi,
Jayesh Verma,
Pinaki Pratim Acharjya

**Abstract:**

**Keywords:**
Image segmentation,
edge Detection,
noisy images,
spatialfilters,
stochastic gradient kernel.

##### 2719 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

**Authors:**
Tarun Kumar Rawat,
Abhirup Lahiri,
Ashish Gupta

**Abstract:**

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.

**Keywords:**
Single-ended input differential amplifier,
Noise,
stochastic differential equation,
mean and variance.

##### 2718 A Scenario-Based Approach for the Air Traffic Flow Management Problem with Stochastic Capacities

**Authors:**
Soumia Ichoua

**Abstract:**

In this paper, we investigate the strategic stochastic air traffic flow management problem which seeks to balance airspace capacity and demand under weather disruptions. The goal is to reduce the need for myopic tactical decisions that do not account for probabilistic knowledge about the NAS near-future states. We present and discuss a scenario-based modeling approach based on a time-space stochastic process to depict weather disruption occurrences in the NAS. A solution framework is also proposed along with a distributed implementation aimed at overcoming scalability problems. Issues related to this implementation are also discussed.

**Keywords:**
Air traffic management,
sample average approximation,
scenario-based approach,
stochastic capacity.

##### 2717 A Stochastic Diffusion Process Based on the Two-Parameters Weibull Density Function

**Authors:**
Meriem Bahij,
Ahmed Nafidi,
Boujemâa Achchab,
Sílvio M. A. Gama,
José A. O. Matos

**Abstract:**

**Keywords:**
Diffusion process,
discrete sampling,
likelihood
estimation method,
simulation,
stochastic diffusion equation,
trends
functions,
bi-parameters Weibull density function.

##### 2716 PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays

**Authors:**
Zixin Liu,
Jianjun Jiao Wanping Bai

**Abstract:**

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

**Keywords:**
Stochastic recurrent neural networks,
pth moment exponential stability,
distributed time delays.

##### 2715 Data Envelopment Analysis under Uncertainty and Risk

**Authors:**
P. Beraldi,
M. E. Bruni

**Abstract:**

**Keywords:**
DEA,
Stochastic Programming,
Ex-ante evaluation
technique,
Conditional Value at Risk.

##### 2714 Modeling and Simulating Reaction-Diffusion Systems with State-Dependent Diffusion Coefficients

**Authors:**
Paola Lecca,
Lorenzo Dematte,
Corrado Priami

**Abstract:**

The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work a mathematical treatment of diffusion that can be incorporated in a stochastic algorithm simulating the dynamics of a reaction-diffusion system is presented. The movement of a molecule A from a region i to a region j of the space is represented as a first order reaction Ai k- ! Aj , where the rate constant k depends on the diffusion coefficient. The diffusion coefficients are modeled as function of the local concentration of the solutes, their intrinsic viscosities, their frictional coefficients and the temperature of the system. The stochastic time evolution of the system is given by the occurrence of diffusion events and chemical reaction events. At each time step an event (reaction or diffusion) is selected from a probability distribution of waiting times determined by the intrinsic reaction kinetics and diffusion dynamics. To demonstrate the method the simulation results of the reaction-diffusion system of chaperoneassisted protein folding in cytoplasm are shown.

**Keywords:**
Reaction-diffusion systems,
diffusion coefficient,
stochastic simulation algorithm.

##### 2713 Passivity Analysis of Stochastic Neural Networks With Multiple Time Delays

**Authors:**
Biao Qin,
Jin Huang,
Jiaojiao Ren,
Wei Kang

**Abstract:**

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

**Keywords:**
Passivity,
Stochastic neural networks,
Multiple time
delays,
Linear matrix inequalities (LMIs).

##### 2712 Advanced Stochastic Models for Partially Developed Speckle

**Authors:**
Jihad S. Daba (Jean-Pierre Dubois),
Philip Jreije

**Abstract:**

**Keywords:**
Doubly stochastic filtered process,
Poisson point process,
segmentation,
speckle,
ultrasound

##### 2711 Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay

**Authors:**
Yong Li

**Abstract:**

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

**Keywords:**
Mild solution,
Convex multivalued map,
Neutral
stochastic differential inclusions.