Social Motives and Expectations in One-Shot Asymmetric Prisoner's Dilemmas

We propose a formal-behavioral framework with 3 components: nonselfish motives, expectations about others' nonselfish motives, and a game-theoretic component. For nonselfish motives, 3 nonstandard utility models representing altruism, inequality aversion, and norms are considered. Expectations are modeled as certain versus uncertain expectations. The game-theoretic component predicts behavior of actors and actors' expectations about behaviors of others. This framework is applied to asymmetric one-shot prisoner's dilemmas; predictions are tested experimentally. Formal analyses show that asymmetry provides new predictions through which nonstandard utility-expectation models can be distinguished. Empirical tests show that the inequality aversion model does considerably worse than altruistic and normative variants. Statistical tests for own motives, expected motives, and the association between the two are provided, while accounting for decision noise.     

Random telegraph signals with time dependent capture and emission probabilities: Analytical and numerical results

In this work, we study the noise spectra of random telegraph signals (RTS) with time dependent capture and emission probabilities. The capture and emission probabilities are made time dependent by cyclo-stationary excitation. Rigorous analytical calculations are performed to derive the model equations, and Monte Carlo simulations are performed to explore the noise behavior and validate the analytical model. Two study cases are explored: input signals modeled by periodic square wave and sinusoidal waves. We present clear situations where the integrated noise power is smaller than stationary case for a suitable choice of parameters in both cyclo-stationary inputs studied.     

Probability density function of leaky integrate-and-fire model with Lévy noise and its numerical approximation

We investigate the numerical analysis of leaky integrate-and-fire model with Lévy noise. We consider a neuronal model in which probability density function of a neuron in some potential at any time is modeled by a transport equation. Lévy noise is included due to jumps by excitatory and inhibitory impulses. Due to these jumps the resulting equation is a transport equation containing two integral in right-hand side (jumps). We design, implement, and analyze numerical methods of finite volume type. Some numerical examples are also included.     

Optimal Guaranteed Cost Control of Stochastic Discrete-Time Systems with States and Input Dependent Noise Under Markovian Switching

A problem of robust guaranteed cost control of stochastic discrete-time systems with parametric uncertainties under Markovian switching is considered. The control is simultaneously applied to both the random and the deterministic components of the system. The noise (the random) term depends on both the states and the control input. The jump Markovian switching is modeled by a discrete-time Markov chain and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Using linear matrix inequalities (LMIs) approach, the robust quadratic stochastic stability is obtained. The proposed control law for this quadratic stochastic stabilization result depended on the mode of the system. This control law is developed such that the closed-loop system with a cost function has an upper bound under all admissible parameter uncertainties. The upper bound for the cost function is obtained as a minimization problem. Two numerical examples are given to demonstrate the potential of the proposed techniques and obtained results.     

Stabilization of stochastic systems under Markovian switching

The problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching is considered. The jump Markovian switching is modeled by a discrete-time Markov chain, and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Necessary and sufficient conditions based on linear matrix inequalities (LMI’s) for stochastic stability is obtained. The proposed control law for this stochastic stabilization result depends on the mode of the system as well as the environmental disturbances. The robustness results of such stability concepts against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.     

Effects of random noise in a dynamical model of love

This paper aims to investigate the stochastic model of love and the effects of random noise. We first revisit the deterministic model of love and some basic properties are presented such as: symmetry, dissipation, fixed points (equilibrium), chaotic behaviors and chaotic attractors. Then we construct a stochastic love-triangle model with parametric random excitation due to the complexity and unpredictability of the psychological system, where the randomness is modeled as the standard Gaussian noise. Stochastic dynamics under different three cases of “Romeo’s romantic style”, are examined and two kinds of bifurcations versus the noise intensity parameter are observed by the criteria of changes of top Lyapunov exponent and shape of stationary probability density function (PDF) respectively. The phase portraits and time history are carried out to verify the proposed results, and the good agreement can be found. And also the dual roles of the random noise, namely suppressing and inducing chaos are revealed.     

Stochastic evolution equations with general white noise disturbance

Existence and uniqueness theorems are proved for a general class of stochastic linear abstract evolution equations, with a general type of stochastic forcing term. The abstract evolution equation is modeled using an evolution operator (or 2-parameter semigroup) approach and this includes linear partial differential equations and linear differential delay equations. The stochastic forcing term is modeled by defining an Itô stochastic integral with respect to a Hilbert space-valued orthogonal increments process, which can be used to model both Gaussian and non-Gaussian white noise processes. The theory is illustrated by examples of stochastic partial differential equations and delay equations, which arise in filtering problems for distributed and delay systems.     

A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.     

Pricing American options when asset prices jump

We present a transformation that helps price American options on assets that are modeled by a diffusion as well as a jump component. The presence of a jump component circumvents some shortcomings of the Black-Scholes model. The proposed transformation essentially transforms the arising free-boundary partial integro-differential equation (PIDE) into a sequence of fixed-boundary PIDEs which are much easier to solve. Finally, we provide numerical results illustrating convergence of the scheme and comparisons to other methods.     

Stochastic virus dynamics with Beddington-DeAngelis functional response

Stochastic virus dynamics modeled by a system of stochastic differential equations with Beddington-DeAngelis functional response and driven by white noise is investigated. The global existence of positive solutions and the existence of stationary distribution are proved. Upper and lower bounds of the pathwise and asymptotic moments for the positive solutions are sharply estimated. The absorbing property in time average is shown and the moment Lyapunov exponents are proved to be nonpositive.     

On noise modeling in a nerve fibre

We present a novel mathematical approach to model noise in dynamical systems. We do so by considering the dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in a variable representing the transmembrane current can be effectively modeled as fluctuations in the model parameters corresponding to electric resistance and capacitance of the membrane. These fluctuations may account for the interactions between the membrane and the surrounding (physiological) solution as well as for the thermal effects. The proposed approach to model noise in a nerve fibre is an alternative to the standard technique based on the consideration of additive stochastic current perturbation (the Langevin type equations) and differs from it in important mathematical aspects, particularly, it points out to the non-Markov dynamics of transmembrane potential. Our scheme relates to a time scale which is shorter than the relaxation times of involved physiological processes.     

Hierarchical entropy analysis for biological signals

We develop a hierarchical entropy (HE) method to quantify the complexity of a time series based on hierarchical decomposition and entropy analysis. The proposed method is applied to the Gaussian white noise and the 1/f noise. We prove that the difference frequency components of the Gaussian white noise with the same scale factor have the same value of entropies, and the values decline as the scale factor increases. We also apply the HE method to the 1/f noise, and prove mathematically that a lower frequency component of a 1/f noise is also a 1/f noise and verify numerically that a higher frequency component of a 1/f random vector is approximately equal to a Gaussian random vector. The theoretical results are confirmed by numerical results. Moreover, we show that the HE method is an efficient method to analyze heartbeat signals by applying it to the cardiac interbeat interval time series of healthy young and elderly subjects, congestive heart failure (CHF) subjects and atrial fibrillation (AF) subjects.     

Critical phenomena in evolving networks: Ferromagnetic phase transition in evolving network of stochastic cellular automata

It is shown by MC simulations that ferromagnetic system modeled by cellular automata with synchronously rewired interconnections changes critically when preference in rewiring is added – the system becomes resistant against stochastic noise. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Strategic Defense in Stochastic Networks

This paper deals with the detection and prediction of losses due to cyber attacks waged on vital networks. The accumulation of losses to a network during a series of attacks is modeled by a 2-dimensional monotone random walk process as observed by an independent delayed renewal process. The first component of the process is associated with the number of nodes (such as routers or operational sites) incapacitated by successive attacks. Each node has a weight associated with its incapacitation (such as loss of operational capacity or financial cost associated with repair), and the second component models the cumulative weight associated with the nodes lost. Each component has a fixed threshold, and crossing of a threshold by either component represents the network entering a critical condition. Results are given as joint functionals of the predicted time of the first observed threshold crossing along with the values of each component upon this time.     

跳跃——-扩散型欧式加权几何平均价格亚式期权定价

在亚式期权定价理论的基础上, 对期权的标的资产价格引入跳跃---扩散过程进行建模, 用几何Brown运动描述其常态连续变动, 用Possion过程刻画资产价格受新信息和稀有偶发事件的冲击发生跳跃的记数过程, 用对数正态随机变量描述跳跃对应的跳跃幅度, 在模型限定下运用Ito-Skorohod微分公式和等价鞅测度变换, 导出欧式加权几何平均价格亚式期权封闭形式的解析定价公式     

Robust Control of Markovian Switching Stochastic Systems with Noise Dependent States and Inputs

A problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching and random diffusion (noise) is considered. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. Sufficient conditions based on linear matrix inequalities (LMI's) for stochastic stability is obtained. The robustness results of such stability concept against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.     

Transient behaviour of semilinear stochastic systems with random parameters

The transient solution of a class of nonautonomous, stochastic differential equations with given random initial conditions is studied. The considered evolution equation is characterized by the presence of a deterministic linear term and of a random nonlinear term whose parameters can be modeled by random processes of Rice noise type. Analytical approximated expressions for the first- and second-order moments and for the probability density of the solution process are derived and are applied to determine the statistical properties of a class of stochastic nonlinear oscillators.     

Near-optimal controls of differential systems with switching and random jumps subject to fast switching and wideband noise perturbation

This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching. The random switching is modeled by a continuous-time, time-inhomogeneous Markov chain. Under broad conditions, it is shown that there is an associated limit problem, which is a switching jump diffusion. Using near-optimal controls of the limit system, we then build controls for the original systems. It is shown that such constructed controls are nearly optimal.     

多跳-扩散模型与脆弱欧式期权定价

本文对期权的标的资产价格和合约空头方的资产-债务比(Assets-to-Liabilities)引入有多个跳风险源的跳-扩散过程(Jump-Diffusion Process)进行建模.用几何Brown运动描述其常态连续运动的情形,用多个不同强度的Poisson过程描述遭受各种新信息或稀有偶发事件所触发的各种跳发生的记数过程,用多个不同的对数正态随机变量描述各种跳所对应的跳幅度,并假定跳风险是可分散的.在模型限定下,我们应用Ito引理和等价鞅测度变换,导出了公司价值型信用风险欧式期权一股化的封闭形式的解析定价公式,推广了经典的结构信用风险期权定价以及状态变量带单跳的跳-扩散情形,同时也从定量的角度完善了Zhou(2001)和Lobo(1999)的工作.     

Coupled fluid-structure interaction analysis

A general-purpose fluid-structure interaction capability which can be used in analyzing internal acoustic problems in automobiles and aircraft has been formulated. This capability has become an important issue in the last few years because of the emphasis that has been placed on noise control in all vehicles. A variety of output features that are needed by the analyst in identifying the causes of the acoustic problems have been studied and implemented. The fluid (air) is modeled as an inviscid, irrotational fluid with pressure variables as the degrees of freedom. An acoustic absorber element and an acoustic barier element are also implemented.