stability of a novel stochastic epidemic model with double epidemic hypothesis abstract in this paper a novel sir disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation we present the stability conditions of the disease free equilibrium of the sir model without stochastic perturbation and with stochastic perturbation we obtain the deterministic stability threshold 1 and 2 of the disease free equilibrium under which the disease free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible the results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model

econometric analysis of multivariate realised qml estimation of the covariation of equity prices under asynchronous trading estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading in this paper we develop a multivariate realised quasi likelihood qml approach carrying out inference as if the observations arise from an asynchronously observed vector scaled brownian model observed with error under stochastic volatility the resulting realised qml estimator is positive semi definite uses all available data is consistent and asymptotically mixed normal the quasi likelihood is computed using a kalman filter and optimised using a relatively simple em algorithm which scales well with the number of assets we derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence we show how to make itobtain the non parametric efficiency bound for this problem the estimator is also analysed usingmonte carlo methods and applied to equity data with varying levels of liquidity

a mean extinction time estimate for a stochastic lotka volterra predator prey model the investigation of interacting population models has long been and will continue to be one of the dominant subjects in mathematical ecology moreover the persistence and extinction of these models is one of the most interesting and important topics because it provides insight into their behavior the mean extinction time depends on the initial population size and satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence finding analytical solutions poses severe problems except in a few simple cases so we can only compute numerical approximations an idea already mentioned in sharp and allen 1998 1 in this paper we study a stochastic lotka volterra model allen 2007 2 p 149 we prove the nonnegative character of its solutions for the corresponding backward kolmogorov differential equation we propose a finite element method whose matlab code is offered in the appendix and finally we make a direct comparison between predictions and numerical simulations of stochastic differential equations sdes

fluctuation theorems for quantum master equations a quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i e a quantum master equation qme quantum trajectories and their associated entropy heat and work appear naturally by transforming the qme to a time dependent liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem a quantum integral fluctuation theorem a steady state fluctuation theorem and the jarzynski relation are derived in a similar way as for classical stochastic dynamics

extinction time for stochastic population models the analysis of interacting population models is the subject of much interest in mathematical ecology moreover the persistence and extinction of these models is one of the most interesting and important topics because it provides insight into their behavior the mean extinction time for stochastic population models considered in this paper depends on the initial population size and satisfies a stationary partial differential equation related to the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients in this communication we review several papers where we have proposed some numerical techniques in order to estimate the mean extinction time for stochastic population models besides we will compare the theoretical predictions and numerical simulations for stochastic differential equations sdes this work can be viewed as a unified review of the contributions de la hoz and vadillo 2012 de la hoz et al 2014 and doubova and vadillo 2014

dynamics of non autonomous stochastic gilpin ayala competition model with time varying delays in this paper the non autonomous stochastic gilpin ayala competition model with time dependent delay is considered we prove existence and uniqueness of the global positive solution and various properties of that solution such as boundedness moment and pathwise estimation extinction non persistence in time average and weak persistence in addition we give a special case of the considered system and impose its properties all studied features are natural requirements from the biological point of view furthermore examples with numerical simulations are given to illustrate our results

test of fluctuation theorems in non markovian open quantum systems we study fluctuation theorems for open quantum systems with a non markovian heat bath using the approach of quantum master equations and examine the physical quantities that appear in those fluctuation theorems the approach of markovian quantum master equations to the fluctuation theorems was developed by esposito and mukamel phys rev e 73 046129 2006 we show that their discussion can be formally generalized to the case of a non markovian heat bath when the local system is linearly connected to a gaussian heat bath with the spectrum distribution of the drude form we found by numerically simulating the spin boson model in non markovian regime that the detailed balance condition is well satisfied except in a strongly nonequilibrium transient situation and hence our generalization of the definition of the entropy production is almost always legitimate therefore our generalization of the fluctuation theorem seems meaningful in wide regions

fluctuation theorems work is not an observable the characteristic function of the work performed by an external time dependent force on a hamiltonian quantum system is identified with the time ordered correlation function of the exponentiated system s hamiltonian a similar expression is obtained for the averaged exponential work which is related to the free energy difference of equilibrium systems by the jarzynski work theorem

the tasaki crooks quantum fluctuation theorem starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in talkner et al 2007 phys rev e 75 050102 preprint cond mat 0703213 the quantum version of the crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse fourier transformation

fitting a two phase threshold multiplicative error model abstract the recent literature on financial time series analysis has devoted considerable attention to nonnegative time series such as financial durations realized volatility and squared returns the class of models referred to as the multiplicative error models mem is particularly suited to model such nonnegative time series we develop a lack of fit test for fitting a two phase threshold model for the conditional mean function in an mem the proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models we evaluate the test in a simulation study the testing procedure is illustrated by using two data examples

dynamic of a stochastic predator prey population abstract a stochastic predator prey model is studied firstly we prove the existence uniqueness and positivity of the solution then we show the upper bounds for moments and growth rate of population in some cases the growth rate is negative and the population dies out rapidly the paper ends with some reviews for the paper 13

quantum work fluctuation theorem exact case study for a perturbed oscillator we analytically explore the fluctuation of the work induced entropy production of an externally perturbed quantum harmonic oscillator interacting with several reservoirs the quantum fluctuation of the work amounts to a non gaussian fluctuation of the entropy production which interpolates the gaussian and the poissonian distributions at high and low temperature regimes also it is shown that the corresponding fluctuation theorem symmetry is rigorously satisfied

unified treatment of the quantum fluctuation theorem and the jarzynski equality in terms of microscopic reversibility there are two related theorems which hold even in far from equilibrium namely fluctuation theorem and jarzynski equality fluctuation theorem states the existence of symmetry of fluctuation of entropy production while the jarzynski equality enables us to estimate the free energy change between two states by using irreversible processes on the other hand the relationship between these theorems was investigated by crooks phys rev e 60 2721 1999 for the classical stochastic systems in this paper we derive quantum analogues of fluctuation theorem and jarzynski equality in terms of microscopic reversibility in other words the quantum analog of the work by crooks is presented also for the quasiclassical langevin system microscopically reversible condition is confirmed

comparing stochastic lotka volterra predator prey models abstract the phenomenology of population extinction is one of the central themes in population biology which it is an inherently stochastic event in the present investigation we study this problem for three different stochastic models built from a single lotka volterra deterministic model more concretely we study their mean extinction time which satisfies the backward kolmogorov differential equation a linear second order partial differential equation with variable coefficients hence we can only compute numerical approximations we suggest a finite element method using freefem our analysis and numerical results allow us to conclude that there are important differences between the three models these differences enable us to choose the most natural way to turn a the deterministic model into a stochastic model

modeling returns volatility realized garch incorporating realized risk measure abstract this study applies realized garch models by introducing several risk measures of intraday returns into the measurement equation to model the daily volatility of e mini s p 500 index futures returns besides using the conventional realized measures realized volatility and realized kernel as our benchmarks we also use generalized realized risk measures realized absolute deviation and two realized tail risk measures realized value at risk and realized expected shortfall the empirical results show that realized garch models using the generalized realized risk measures provide better volatility estimation for the in sample and substantial improvement in volatility forecasting for the out of sample in particular the realized expected shortfall performs best for all of the alternative realized measures our empirical results reveal that future volatility may be more attributable to present losses risk measures the results are robust to different sample estimation windows

multivariate realised kernels consistent positive semi definite estimators of the covariation of equity prices with noise and non synchronous trading we propose a multivariate realised kernel to estimate the ex post covariation of log prices we show this new consistent estimator is guaranteed to be positive semi definite and is robust to measurement noise of certain types and can also handle non synchronous trading it is the first estimator which has these three properties which are all essential for empirical work in this area we derive the large sample asymptotics of this estimator and assess its accuracy using a monte carlo study we implement the estimator on some us equity data comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals we show the new estimator is substantially more precise

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

characteristics of the volatility in the korea composite stock price index abstract we empirically analyze the time series of the korea composite stock price index kospi from march of 1992 to february of 2007 using methods from the hydrodynamic turbulence to this end we focus on characteristics of the return and volatility which are respectively the price change and a measure of the financial market fluctuation over a time interval with these we show that the non gaussian probability distribution of the return can be modeled by the convolution of the conditional probability distribution of the return given the volatility and the distribution of the volatility per se from this model we suggest that the non gaussian characteristic of the return results from the fluctuation of the volatility that is a large return is partly if not entirely due to the market fluctuation in a long time scale influencing the fluctuation in a short time scale via net information flow we further show that the volatility has a multi fractal property which resembles the multifractality of the energy dissipation in the turbulence

asymptotic behavior and stability of a stochastic model for aids transmission a stochastic model for aids transmission is presented in this paper the existence and uniqueness of its solution is proved and the solution belongs to an interval satisfying the actual condition furthermore the disease equilibrium can be demonstrated to be existent and both its almost surely exponential stability and its pth moment exponential stability can be concluded based on parameter analysis the first quadrant can be integrated into several parts according to the comparison between almost surely exponential stability and pth moment exponential stability and the potential meaning of the stability is further demonstrated finally based on the above theoretical analysis some conditions for aids to decrease and then to die out are obtained by computer simulation

testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression abstract broad classes of diagnostics for serial correlation and or dynamic conditional heteroskedasticity of regression disturbances are considered the classes include statistics with good power against strongly dependent alternatives along with the usual ones that test against weak dependence and many others limiting null distributions are obtained under mild conditions on the dependence structure of the alternative against which the test is derived on moments of the disturbances and on the regressors the various test statistics have a similar overall structure and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives the difference can be slight if the fast fourier transform is used

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

predicting population extinction from early observations of the lotka volterra system abstract population extinction is one of the central themes in population biology we propose a statistical algorithm for long term prediction of an extinction event in the paradigmatic predator prey model the algorithm is based on noisy and sporadic observations of the lotka volterra lv system at the early stages of its evolution when the system is still very far from extinction there are two stages in the algorithm first the unknown parameters reaction rates of the lv system are estimated using the approximate bayesian computation method then an analytical expression for the time scale of extinction which involves the estimated parameters is applied to compute the probability density function of extinction time the proposed algorithm is validated by numerical simulations for the case of a stochastic lv system specified by the birth death rate equations the algorithm can be seen as an initial step in the quest for long term prediction of rare catastrophic events in complex stochastic dynamic systems epidemics host parasite dynamics enzyme kinetics dynamic trading etc

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

filtering and forecasting with misspecified arch models i getting the right variance with the wrong model this paper investigates the properties of the conditional covariance estimates generated by a misspecified arch model for example suppose that we observe a diffusion process at discrete time intervals of length h for each h we use a garch 1 1 model to estimate the instantaneous conditional covariance matrix of the diffusion under mild regularity conditions the difference between these conditional covariance estimates and the true conditional covariance converges to zero in probability as h 0 many other arch models for example exponential arch have similar consistency properties this may well account for the success of arch models in short term forecasting using high frequency data since even misspecified arch models can produce good estimates of volatility

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

forecasting s p 100 volatility the incremental information content of implied volatilities and high frequency index returns the information content of implied volatilities and intraday returns is compared in the context of forecasting index volatility over horizons from 1 to 20 days forecasts of two measures of realized volatility are obtained after estimating arch models using daily index returns daily observations of the vix index of implied volatility and sums of squares of 5 min index returns the in sample estimates show that nearly all relevant information is provided by the vix index and hence there is not much incremental information in high frequency index returns for out of sample forecasting the vix index provides the most accurate forecasts for all forecast horizons and performance measures considered the evidence for incremental forecasting information in intraday returns is insignificant

a multiple indicators model for volatility using intra daily data many ways exist to measure and model financial asset volatility in principle as the frequency of the data increases the quality of forecasts should improve yet there is no consensus about a true or best measure of volatility in this paper we propose to jointly consider absolute daily returns daily high low range and daily realized volatility to develop a forecasting model based on their conditional dynamics as all are non negative series we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function the estimation results show significant interactions between the indicators we also show that one month ahead forecasts match well both in and out of sample the market based volatility measure provided by an average of implied volatilities of index options as measured by vix

incorporating overnight and intraday returns into multivariate garch volatility models abstract we propose and evaluate mixed frequency multivariate garch models for forecasting low frequency weekly volatility based on high frequency intraday returns at 5 minute intervals and on the overnight returns the low frequency conditional volatility matrix is modeled as a weighted sum of an intraday and an overnight component the components are specified as multivariate garch processes of the bekk type adapted to the mixed frequency data setting and may enter the model as two separate components or as a single one the models may further be extended by a nonparametrically estimated slowly varying long run volatility matrix we evaluate the models in and out of sample using the 5 minute and overnight returns on four djia stocks axp ge hd and ibm from january 1988 to november 2014 and find that they systematically dominate a variety of models that only use lower frequency data weekly daily or close to open and open to close returns

the econometrics of ultra high frequency data ultra high frequency data is defined to be a full record of transactions and their associated characteristics the transaction arrival times and accompanying measures can be analyzed as marked point processes the acd point process developed by engle and russell 1998 is applied to ibm transactions arrival times to develop semiparametric hazard estimates and conditional intensities combining these intensities with a garch model of prices produces ultra high frequency measures of volatility both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro structure

strong convergence of euler type methods for nonlinear stochastic differential equations traditional finite time convergence theory for numerical methods applied to stochastic differential equations sdes requires a global lipschitz assumption on the drift and diffusion coefficients in practice many important sde models satisfy only a local lipschitz property and since brownian paths can make arbitrarily large excursions the global lipschitz based theory is not directly relevant in this work we prove strong convergence results under less restrictive conditions first we give a convergence result for euler maruyama requiring only that the sde is locally lipschitz and that the pth moments of the exact and numerical solution are bounded for some p 2 as an application of this general theory we show that an implicit variant of euler maruyama converges if the diffusion coefficient is globally lipschitz but the drift coefficient satisfies only a one sided lipschitz condition this is achieved by showing that the implicit method has bounded moments and may be viewed as an euler maruyama approximation to a perturbed sde of the same form second we show that the optimal rate of convergence can be recovered if the drift coefficient is also assumed to behave like a polynomial

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

persistence and extinction in stochastic non autonomous logistic systems this paper studies two widely used stochastic non autonomous logistic models for the first system sufficient conditions for extinction non persistence in the mean weak persistence and stochastic permanence are established the critical number between weak persistence and extinction is obtained for the second system sufficient criteria for extinction non persistence in the mean weak persistence in the mean strong persistence in the mean and stochastic permanence are established the critical number between weak persistence in the mean and extinction is obtained it should be pointed out that this research is systematical and complete in fact the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper

fluctuation theorems for non markovian quantum processes exploiting previous results on markovian dynamics and fluctuation theorems we study the consequences of memory effects on single realizations of nonequilibrium processes within an open system approach the entropy production along single trajectories for forward and backward processes is obtained with the help of a recently proposed classical like non markovian stochastic unravelling which is demonstrated to lead to a correction of the standard entropic fluctuation theorem this correction is interpreted as resulting from the interplay between the information extracted from the system through measurements and the flow of information from the environment to the open system due to memory effects single realizations of a dynamical process are no longer independent and their correlations fundamentally affect the behavior of entropy fluctuations

global asymptotic stability of a stochastic delayed predator prey model with beddington deangelis functional response this paper is concerned with a stochastic predator prey system with beddington deangelis functional response and time delay sufficient conditions for global asymptotic stability of the positive equilibrium point are established the result demonstrates that the delay is harmless for global stability of the stochastic system in some cases some figures are given to validate the analytical results

chasing volatility a persistent multiplicative error model with jumps abstract persistence and unpredictable large increments characterize the volatility of financial returns we propose the multiplicative error model with volatility jumps mem j to describe and predict the probability and the size of these extreme events under the mem j the conditional density of the realized measure is a countably infinite mixture of gamma and kappa distributions with closed form conditional moments we derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises the mem j improves over other models with fat tails