finite element approximation of stochastic partial differential equations driven by poisson random measures of jump type the paper deals with stochastic partial differential equations driven by poisson random measures of jump type and their numerical approximation we investigate the accuracy of space and time approximation as space approximation we consider finite elements and as time approximation the implicit euler scheme

stochastic integrators with stationary independent increments lipschitzian stochastic differential equations driven by a process with stationary independent increments permit a priori growth and stability estimates up to any sure time and the solutions depend differentiably on parameters provided the levy measure of the driving term has suitable moments

chaos synchronization of different chaotic systems subjected to input nonlinearity abstract in this paper a unified mathematical expression describing a class of synchronization systems is presented for which the problem of chaos synchronization between different chaotic systems with input nonlinearity has been studied based on lyapunov stability theory a sliding mode controller and some generic sufficient conditions for global asymptotic synchronization are designed such that the error dynamics of two different chaotic motions satisfy stability in the lyapunov sense in spite of the input nonlinearity this technique is applied to achieve chaos synchronization of three pairs of different chaotic systems lorenz chen chen liu and liu lorenz in drive response structure the numerical simulation results demonstrate the validity and feasibility of the proposed controller

chaos synchronization and chaos anticontrol of a suspended track with moving loads abstract in this paper we first study the chaotic synchronization phenomenon of the suspended track with moving load system and then the transient response of chaos synchronization the lyapunov exponent is utilized to prove the chaos synchronization but under certain conditions it is more complicated next we study the synchronization of autonomous and non autonomous systems we find that slave systems cannot be synchronized with master system for certain time excitations no matter how large a is next the phase synchronization between them will be studied an application of chaos synchronization and secure communication is presented finally in order to increase the chaos phenomena we use anticontrol constant torque periodic torque periodic impulse signal time delay function and adaptive control are used successfully to control the state from order to chaos

adaptive weak approximation of diffusions with jumps this work develops adaptive time stepping algorithms for the approximation of a functional of a diffusion with jumps based on a jump augmented monte carlo euler maruyama method which achieve a prescribed precision the main result is the derivation of new expansions for the time discretization error with computable leading order term in a posteriori form which are based on stochastic flows and discrete dual backward functions combined with proper estimation of the statistical error they lead to efficient and accurate computation of global error estimates extending the results by a szepessy r tempone and g e zouraris comm pure appl math 54 2001 pp 1169 1214 adaptive algorithms for either deterministic or trajectory dependent time stepping are proposed numerical examples show the performance of the proposed error approximations and the adaptive schemes

survival analysis of a stochastic service resource mutualism model in a polluted environment with pulse toxicant input abstract in this paper taking the white noises markovian switching and levy jumps into account a stochastic service resource mutualism model in a polluted environment with pulse toxicant input is proposed and analyzed the critical value between persistence in the mean and extinction for each species is obtained several numerical simulations are also introduced to illustrate the theoretical results the results reveal that random perturbations the impulsive period and the toxicant input amount each time have close relationships with the persistence and extinction of the species

asymptotics beats monte carlo the case of correlated local vol baskets we consider a basket of options with both positive and negative weights in the case where each asset has a smile i e evolves according to its own local volatility and the driving brownian motions are correlated in the case of positive weights the model has been considered in a previous work by avellaneda boyer olson busca and friz we derive highly accurate analytic formulas for the prices and the implied volatilities of such baskets the relative errors are of order 10 4 or better for t 10 3 for t 2 and 10 2 for t 10 years the computational time required to implement these formulas is under two seconds even in the case of a basket on 100 assets the combination of accuracy and speed makes these formulas potentially attractive both for calibration and for pricing in comparison simulation based techniques are prohibitively slow in achieving a comparable degree of accuracy thus the present work opens up a new paradigm in which asymptotics may arguably be used for pricing as well as for calibration 2014 wiley periodicals inc

dynamics of an imprecise sirs model with levy jumps abstract sudden environmental perturbations may affect population dynamics parameters of mathematical models can also be imprecise due to uncertainties and unknown data how sudden environmental noise and parameter imprecision influence the dynamics of epidemic systems remains unclear this paper studies a stochastic susceptible infected recovered susceptible sirs model that includes levy jumps and interval parameters we prove that the model has a unique global positive solution sufficient conditions for persistence and extinction of the disease are obtained large noise intensity is able to suppress the emergence of disease outbreaks numerical simulations are carried out to show the influence of stochastic noise on disease dynamics these results suggest that levy jumps and imprecise parameters can greatly affect the long term behavior of the epidemic system

the direct richardson p th order drp schemes a new class of time integration schemes for stochastic differential equations we describe a new family of weak p th order accurate sde time integration schemes called the direct richardson p th order accurate drp schemes the drp schemes use the idea of richardson extrapolation on euler time steps performed by way of an acceptance rejection algorithm previous applications of richardson extrapolation to the euler scheme are applicable only when the objective is to estimate a functional of the final distribution of the process in contrast provided that the diffusion matrix is strictly positive definite the drp class of schemes can be used in all applications which require a weak sde time integration scheme numerical results have been obtained and a comparison is made between the second and third order accurate drp schemes and other modern sde time integration schemes indicating that the drp schemes incur less error than standard algorithms based on ito taylor expansions and have similar computational efficiency finally we provide a proof of the convergence properties of the drp schemes

a general control variate method for option pricing under levy processes abstract we present a general control variate method for simulating path dependent options under levy processes it is based on fast numerical inversion of the cumulative distribution functions and exploits the strong correlation of the payoff of the original option and the payoff of a similar option under geometric brownian motion the method is applicable for all types of levy processes for which the probability density function of the increments is available in closed form numerical experiments confirm that our method achieves considerable variance reduction for different options and levy processes we present the applications of our general approach for asian lookback and barrier options under variance gamma normal inverse gaussian generalized hyperbolic and meixner processes

on a stochastic delayed predator prey model with levy jumps this note is concerned with a stochastic delayed predator prey system with levy jumps under some simple conditions sufficient and necessary conditions for stability in time average and extinction of each species are obtained

extinction and persistence of a stochastic nonlinear sis epidemic model with jumps abstract in this paper brownian motion and l e vy jumps are introduced to a sis type epidemic model with nonlinear incidence rate the dynamical behavior of the considered model is investigated in order to reveal the extinction and permanence of the disease two threshold values r 0 r 0 are showed we find that if r 0 1 the disease may die out and when r 0 1 the disease may be persistent finally the numerical simulations are presented to illustrate our mathematical results

the euler scheme with irregular coefficients weak convergence of the euler scheme for stochastic differential equations is established when coefficients are discontinuous on a set of lebesgue measure zero the rate of convergence is presented when coefficients are holder continuous monte carlo simulations are also discussed

weak approximations and extrapolations of stochastic differential equations with jumps numerical discretization schemes are developed to approximate functionals of stochastic differential equations with jumps and the convergence is shown to have an appropriate order for the euler scheme and the second order weak scheme the leading coefficient of their global errors are determined by the stochastic taylor expansion based on the error expression the extrapolation technique can be applied to get a higher order convergence numerical examples are provided to compare various weak schemes and extrapolations

an approximation formula for basket option prices under local stochastic volatility with jumps this paper develops a new approximation formula for pricing basket options in a local stochastic volatility model with jumps in particular the model admits local volatility functions and jump components in not only the underlying asset price processes but also the volatility processes to the best of our knowledge the proposed formula is the first one which achieves an analytical approximation for the basket option prices under this type of the models moreover in numerical experiments we provide approximate prices for basket options on the wti futures and brent futures based on the parameters through calibration to the plain vanilla option prices and confirm the validity of our approximation formula

two theorems of generalized unsynchronization for coupled chaotic systems generalized chaos synchronization has been widely studied and many control methods have been presented but up to now no criterion has been given for generalized unsynchronization the generalized unsynchronization means that the state variables of two coupled chaotic systems cannot approach generalized synchronization in this paper we propose two theorems which give the criteria of generalized unsynchronization for two different chaotic dynamic systems with whatever large strength of linear coupling two simulated examples are also given

a new algorithm for solving nearly penta diagonal toeplitz linear systems a new numerical algorithm for solving nearly penta diagonal toeplitz linear systems is presented the algorithm is suited for implementation using computer algebra systems cass such as matlab macsyma and maple numerical examples are given in order to illustrate the efficiency of our algorithm

numerical study of interacting particles approximation for integro differential equations the paper develops a numerical method based on the interacting particles approximation propagation of chaos for the solution of a large class of evolution problems involving the fractional laplacian operator and a non local quadratic type non linearity coupled stochastic differential equations driven by levy symmetric a stable processes are integrated numerically using euler s method and the solutions of the governing equations are obtained from their statistics the method is tested on several one and two dimensional examples and established analytical properties of the solutions are verified for the numerical approximates when they are available for initial conditions that are either integrable or monotone bounded functions it is shown that these methods represent viable tools for constructing the solution to the cauchy problem

optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps abstract in this paper the optimal harvesting of a stochastic delay tri trophic food chain model with levy jumps is considered we introduce two kinds of environmental perturbations in this model one is called white noise which is continuous and is described by a stochastic integral with respect to the standard brownian motion and the other one is jumping noise which is modeled by a levy process under some mild assumptions the critical values between extinction and persistent in the mean of each species are established the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the optimal harvesting effort and the maximum of sustainable yield are also obtained we utilize the ergodic method to discuss the optimal harvesting problem the results show that white noises and levy noises significantly affect the optimal harvesting policy while time delays is harmless for the optimal harvesting strategy in some cases at last some numerical examples are introduced to show the validity of our results

numerical analysis for jump diffusion differential equations in this paper euler approximation is introduced for a broad class of jump diffusion equations and the numerical approximation is studied for multidimensional jump diffusion processes we prove that numerical solutions based on the euler scheme will converge to the analytic solution if both remain within a compact set both of analytic solution and the approximate solution are bounded in probability the numerical solution is solved by this method when the linear growth and global lipschitz conditions are not satisfied by the system an example is studied to illustrate the results keyword jump diffusion equations euler scheme numerical solution

a general control variate method for multi dimensional sdes an application to multi asset options under local stochastic volatility with jumps models in finance abstract this paper presents a new control variate method for general multi dimensional stochastic differential equations sdes including jumps in order to reduce the variance of monte carlo method our control variate method is based on an asymptotic expansion technique and does not require an explicit characteristic function of sdes this is an extension of previous researches using asymptotic expansions to obtain the control variates for such general models moreover in our control variate method the regression estimators can be chosen for each number of jump times with a stratified sampling and improve the efficiency of the variance reduction this paper also provides the asymptotic bias and variance of our method in terms of its terminal time and a small noise parameter used in an asymptotic expansion method for an application of our method we evaluate multi asset options whose payoffs are expressed as linear functions of the underlying asset price processes in general local stochastic volatility with jumps models and show a calculation scheme of control variates for greeks in numerical experiments we apply the new control variate method to pricing basket spread and average options and delta of basket options under a zabr type local stochastic volatility model with jumps and confirm that our method works very well

single transform formulas for pricing asian options in a general approximation framework under markov processes abstract recently cai song and kou 2015 proposed closed form double transform approximation formulas for prices of both discretely and continuously monitored asian options under the setting of a general continuous time markov chain in this note we analytically invert the z transform and the laplace transform involved in their final results respectively for the discretely and the continuously monitored cases and we obtain explicit single laplace transforms of option prices this reduction in the dimension of numerical integral has meaningful consequences both in computational efficiency and in practical implementation of the formulas extensive numerical experiments illustrate the improved performance of our results

a computational algorithm for solving periodic penta diagonal linear systems in this paper we present a new efficient computational algorithm for solving periodic penta digonal linear systems the implementation of the algorithm using computer algebra systems cas such as maple macsyma mathematica and matlab is straightforward an example is given in order to illustrate the algorithm

optimal harvesting policy of a stochastic two species competitive model with levy noise in a polluted environment abstract as well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development this paper presents the optimal harvesting of a stochastic two species competitive model with levy noise in a polluted environment where the levy noise is used to describe the sudden climate change due to the discontinuity of the levy noise the classical optimal harvesting methods based on the explicit solution of the corresponding fokker planck equation are invalid the object of this paper is to fill up this gap and establish the optimal harvesting policy by using of aggregation and ergodic methods the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained numerical simulations are carried out to support these theoretical results our analysis shows that the levy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly

stochastic solution of fractional fokker planck equations with space time dependent coefficients abstract this paper develops solutions of fractional fokker planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non gaussian levy processes with space time dependent drift diffusion and jump coefficients thus significantly extends magdziarz and zorawik s result in 14 fractional fokker planck equation describing subdiffusion is solved by our result in full generality from perspective of stochastic representation

comparison of semimartingales and levy processes in this paper we derive comparison results for terminal values of d dimensional special semimartingales and also for finite dimensional distributions of multivariate levy processes the comparison is with respect to nondecreasing increasing convex increasing directionally convex and increasing supermodular functions we use three different approaches in the first approach we give sufficient conditions on the local predictable characteristics that imply ordering of terminal values of semimartingales this generalizes some recent convex comparison results of exponential models in math finance 8 1998 93 126 finance stoch 4 2000 209 222 proc steklov inst math 237 2002 73 113 finance stoch 10 2006 222 249 in the second part we give comparison results for finite dimensional distributions of levy processes with infinite levy measure in the first step we derive a comparison result for markov processes based on a monotone separating transition kernel by a coupling argument we get an application to the comparison of compound poisson processes these comparisons are then extended by an approximation argument to the ordering of levy processes with infinite levy measure the third approach is based on mixing representations which are known for several relevant distribution classes we discuss this approach in detail for the comparison of generalized hyperbolic distributions and for normal inverse gaussian processes

general multilevel monte carlo methods for pricing discretely monitored asian options abstract we describe general multilevel monte carlo methods that estimate the price of an asian option monitored at m fixed dates for a variety of processes that can be simulated exactly we prove that for the same computational cost our method yields an unbiased estimator with variance lower than the variance of the standard monte carlo estimator by a factor of order m we show how to combine our approach with the milstein scheme for processes driven by scalar stochastic differential equations and with the euler scheme for processes driven by multidimensional stochastic differential equations numerical experiments confirm that our method outperforms the conventional monte carlo algorithm by a factor proportional to m

chaotic synchronization by the intermittent feedback method this paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient a sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a lyapunov function and differential inequalities numerical simulations for the chaotic chua oscillator are presented to illustrate the theoretical results

on weak approximation of stochastic differential equations through hard bounds by mathematical programming upper and lower hard bounds of the expected value on stochastic differential equations can be obtained with the help of mathematical programming and the dynkin formula without recourse to monte carlo sample paths simulation in this paper we show that feasible solutions of those optimization approaches further provide useful additional information namely feasible solutions provide upper and lower bounds for arbitrary intermediate times and or different initial states we also show that the optimization approach can be applied to stochastic differential equations with a random initial state our theoretical analyses are illustrated by numerical results on the survival probability for a square root diffusion on the moment estimation of a doleans dade stochastic exponential with jumps and on pricing of a barrier basket option under the multiasset black scholes model

strong approximations of stochastic differential equations with jumps this paper is a survey of strong discrete time approximations of jump diffusion processes described by stochastic differential equations sdes it also presents new results on strong discrete time approximations for the specific case of pure jump sdes strong approximations based on jump adapted time discretizations which produce no discretization error in the case of pure jump processes are analyzed the computational complexity of these approximations is proportional to the jump intensity by exploiting a stochastic expansion for pure jump processes higher order discrete time approximations whose computational complexity is not dependent on the jump intensity are proposed for the specific case of pure jump sdes the strong order of convergence of strong taylor schemes is established under weaker conditions than those currently known in the literature

impact of jumps on returns and realised variances econometric analysis of time deformed levy processes in order to assess the effect of jumps on realised variance calculations we study some of the econometric properties of time changed levy processes we show that in general realised variance is an inconsistent estimator of the time change however we can derive the second order properties of realised variances and use these to estimate the parameters of such models our analytic results give a first indication of the degrees of inconsistency of realised variance as an estimator of the time change in the non brownian case further our results suggest volatility is even more predictable than has been shown by the recent econometric work on realised variance

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

optimal simulation schemes for levy driven stochastic differential equations we consider a general class of high order weak approximation schemes for stochastic differential equations driven by levy processes with infinite activity these schemes combine a compound poisson approximation for the jump part of the levy process with a high order scheme for the brownian driven component applied between the jump times the overall approximation is analyzed using a stochastic splitting argument the resulting error bound involves separate contributions of the compound poisson approximation and of the discretization scheme for the brownian part and allows on one hand to balance the two contributions in order to minimize the computational time and on the other hand to study the optimal design of the approximating compound poisson process for driving processes whose levy measure explodes near zero in a regularly varying way this procedure allows to construct discretization schemes with arbitrary order of convergence

closed form expansions of discretely monitored asian options in diffusion models in this paper we propose a closed form asymptotic expansion approach to pricing discretely monitored asian options in general one dimensional diffusion models our expansion is a small time expansion because the expansion parameter is selected to be the square root of the length of monitoring interval this expansion method is distinguished from many other pricing oriented expansion algorithms in the literature because of two appealing features first we illustrate that it is possible to explicitly calculate not only the first several expansion terms but also any general expansion term in a systematic way second the convergence of the expansion is proved rigorously under some regularity conditions numerical experiments suggest that the closed form expansion formula with only a few terms e g four terms up to the third order is accurate fast and easy to implement for a broad range of diffusion models even including those violating the regularity conditions

stochastic wave equation of pure jumps existence uniqueness and invariant measures abstract in this paper we investigate a class of nonlinear damped stochastic hyperbolic equations with jumps the jump component considered here is described as a poisson point process this paper is divided into two parts the first part deals with existence and uniqueness of global weak and strong solutions to this type of equations based on the energy approach the second part devotes to the existence and support of invariant measures corresponding to the weak solution semi group based on markov property of the solution

numerical solution of stochastic differential equations with poisson and levy white noise a fixed time step method is developed for integrating stochastic differential equations sde s with poisson white noise pwn and l evy white noise lwn the method for integrating sde s with pwn has the same structure as that proposed by kim et al phys rev e 76 011109 2007 but is established by using different arguments the integration of sde s with lwn is based on a representation of l evy processes by sums of scaled brownian motions and compound poisson processes it is shown that the numerical solutions of sde s with pwn and lwn converge weakly to the exact solutions of these equations so that they can be used to estimate not only marginal properties but also distributions of functionals of the exact solutions numerical examples are used to demonstrate the applications and the accuracy of the proposed integration algorithms

dynamics of a stochastic population model with allee effect and levy jumps abstract this article formulates and researches a single species stochastic population model with allee effect and levy jumps firstly it is shown that the model has a unique global positive solution then sufficient conditions for extinction and stochastic permanence are obtained finally the growth rate of the solution is estimated the results demonstrate that the levy jumps could change the properties of the model significantly several numerical figures are given to explain the theoretical results

regular dependence on initial data for stochastic evolution equations with multiplicative poisson noise abstract we prove existence uniqueness and lipschitz dependence on the initial datum for mild solutions of stochastic partial differential equations with lipschitz coefficients driven by wiener and poisson noise under additional assumptions we prove g teaux and frechet differentiability of solutions with respect to the initial datum as an application we obtain gradient estimates for the resolvent associated to the mild solution finally we prove the strong feller property of the associated semigroup

a fast and reliable algorithm for evaluating nth order pentadiagonal determinants abstract in the current article we present a fast and reliable algorithm for evaluating n th order pentadiagonal determinants in linear time it is a natural generalization of the detgtri algorithm m el mikkawy a fast algorithm for evaluating n th order tri diagonal determinants j comput appl math 166 2004 581 584 the algorithm is suited for implementation using computer algebra systems cas such as macsyma and maple some illustrative examples are given

product expansion for stochastic jump diffusions and its application to numerical approximation abstract we derive a product expansion of the exponential lie series in terms of a philip hall basis for the chen series corresponding to the stochastic jump diffusion as in sussmann in c i byrnes and a lindquist eds theory and applications of nonlinear control systems north holland amsterdam 1986 pp 323 335 for the deterministic case based on the expansion we establish the stratonovich taylor hall sth schemes such that each scheme involves only the minimum number of multiple stochastic integrals which can be regarded as systems of stochastic differential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy mean square convergence of the sth schemes is shown and numerical examples are provided to illustrate the results

a computational algorithm for solving nearly penta diagonal linear systems an efficient computational algorithm for solving nearly penta diagonal linear systems is presented a problem arising from the spreading of a thin power law fluid subject to periodic boundary conditions illustrates the algorithm

the law of the euler scheme for stochastic differential equations i convergence rate of the distribution function we study the approximation problem ofef x t byef x t n where x t is the solution of a stochastic differential equation x t n is defined by the euler discretization scheme with stept n andf is a given function for smoothf s talay and tubaro have shown that the erroref x t f x t n can be expanded in powers of 1 n which permits to construct romberg extrapolation precedures to accelerate the convergence rate here we prove that the expansion exists also whenf is only supposed measurable and bounded under an additional nondegeneracy condition of hormander type for the infinitesimal generator of x t to obtain this result we use the stochastic variations calculus in the second part of this work we will consider the density of the law ofx t n and compare it to the density of the law ofx t

stationary distribution and ergodicity of a stochastic food chain model with levy jumps abstract in this paper a three species stochastic food chain model with levy jumps is proposed and analyzed sharp sufficient criteria for the existence and uniqueness of an ergodic stationary distribution are established the effects of levy jumps on the existence of the stationary distribution are revealed in some cases the levy jumps could make the stationary distribution appear while in some cases the levy jumps could make the stationary distribution disappear some numerical simulations are introduced to illustrate the theoretical results

an auto realignment method in quasi monte carlo for pricing financial derivatives with jump structures abstract discontinuities are common in the pricing of financial derivatives and have a tremendous impact on the accuracy of quasi monte carlo qmc method while if the discontinuities are parallel to the axes good efficiency of the qmc method can still be expected by realigning the discontinuities to be axes parallel wang tan 2013 succeeded in recovering the high efficiency of the qmc method for a special class of functions motivated by this work we propose an auto realignment method to deal with more general discontinuous functions the k means clustering algorithm a classical algorithm of machine learning is used to select the most representative normal vectors of the discontinuity surface by applying this new method the discontinuities of the resulting function are realigned to be friendly for the qmc method numerical experiments demonstrate that the proposed method significantly improves the performance of the qmc method

noise induced oscillations in an actively mode locked laser oscillations induced by noise are examined for an actively mode locked laser additive noise proportional noise and combined noise are considered spatial noise is approximated by hermite expansions and temporal noise is approximated via an approximation of the variance of the random variable using a fourth order adams bashforth scheme the approach is verified on a sample problem and used to explore the governing equations for a mode locked laser the inclusion of multiplicative noise leads to much wider pulses and much longer intervals between pulses

general optimized lower and upper bounds for discrete and continuous arithmetic asian options we propose an accurate method for pricing arithmetic asian options on the discrete or continuous average in a general model setting by means of a lower bound approximation in particular we derive analytical expressions for the lower bound in the fourier domain this is then recovered by a single univariate inversion and sharpened using an optimization technique in addition we derive an upper bound to the error from the lower bound price approximation our proposed method can be applied to computing the prices and price sensitivities of asian options with fixed or floating strike price discrete or continuous averaging under a wide range of stochastic dynamic models including exponential levy models stochastic volatility models and the constant elasticity of variance diffusion our extensive numerical experiments highlight the notable performance and robustness of our optimized lower bound for different test cases

a delayed vaccinated epidemic model with nonlinear incidence rate and levy jumps abstract a stochastic susceptible infectious recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity vaccination and le vy jumps on the transmission of diseases we first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable lyapunov functions based on the analysis we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system

small time edgeworth type expansions for weakly convergent nonhomogeneous markov chains we consider triangular arrays of markov chains that converge weakly to a diffusion process second order edgeworth type expansions for transition densities are proved the paper differs from recent results in two respects we allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero small time asymptotics are motivated by statistical applications and by resulting approximations for the joint density of diffusion values at an increasing grid of points

estimation of continuous time stochastic volatility models with jumps using high frequency data abstract this paper proposes a method of inference for general stochastic volatility models containing price jumps the estimation is based on treating realized multipower variation statistics calculated from high frequency data as their unobservable fill in asymptotic limits the paper provides easy to check conditions under which the error in estimation resulting from this approximation is o p 1 and additional ones under which it is o p 1 t where t is the number of days in the sample extensive monte carlo analysis shows that the proposed estimation method works well in finite samples provided asymptotic approximations are used the estimation technique is applied to the estimation of two semiparametric models

the euler scheme for levy driven stochastic differential equations in relation with monte carlo methods to solve some integro differential equations we study the approximation problem of ee g x t by ee g bar x t n where x t 0 leq t leq t is the solution of a stochastic differential equation governed by a levy process z t bar x n t is defined by the euler discretization scheme with step fractn with appropriate assumptions we show that the error ee g x t ee g bar x t n can be expanded in powers of frac1n if the levy measure of z has finite moments of order high enough otherwise the rate of convergence is slower and its speed depends on the behavior of the tails of the levy measure the simulation of the increments of z t is also discussed

lmi criteria for robust chaos synchronization of a class of chaotic systems abstract based on the lyapunov stability theory and lmi technique a new sufficient criterion formulated in the lmi form is established in this paper for chaos robust synchronization by linear state feedback approach for a class of uncertain chaotic systems with different parameters perturbation and different external disturbances on both master system and slave system the new sufficient criterion can guarantee that the slave system will robustly synchronize to the master system at an exponential convergence rate meanwhile we also provide a criterion to find out proper feedback gain matrix k that is still a pending problem in literature h zhang x k ma synchronization of uncertain chaotic systems with parameters perturbation via active control chaos solitons and fractals 21 2004 39 47 finally the effectiveness of the two criteria proposed herein is verified and illustrated by the chaotic murali lakshmanan chua system and lorenz systems respectively

dynamics of a stochastic one prey two predator model with levy jumps levy noise of one species increases extinction risk of this species and its predator levy noise of one species has no impact on the extinction or not of its prey in some cases levy noises do not effect the stability in distribution of the model this paper is concerned with a one prey two predator model with both white noises and levy noises we first carry out the almost complete parameters analysis for the model in each case we show that each species is either persistent in the mean or extinct depending on some critical values then we establish the sufficient criteria for stability in distribution of the model finally we use some numerical examples to demonstrate the analytical findings

a note on solving nearly penta diagonal linear systems in this paper a new efficient computational algorithm is presented for solving nearly penta diagonal linear systems based on the use of any penta diagonal linear solver the implementation of the algorithm using computer algebra systems cas such as maple and matlab is straightforward numerical examples are given to illustrate the effectiveness of our method

numerical approximation of some linear stochastic partial differential equations driven by special additive noises this paper is concerned with the numerical approximation of some linear stochastic partial differential equations with additive noises a special representation of the noise is considered and it is compared with general representations of noises in the infinite dimensional setting convergence analysis and error estimates are presented for the numerical solution based on the standard finite difference and finite element methods the effects of the noises on the accuracy of the approximations are illustrated results of the numerical experiments are provided

non gaussian ornstein uhlenbeck based models and some of their uses in financial economics non gaussian processes of ornstein uhlenbeck ou type offer the possibility of capturing important distributional deviations from gaussianity and for flexible modelling of dependence structures this paper develops this potential drawing on and extending powerful results from probability theory for applications in statistical analysis their power is illustrated by a sustained application of ou processes within the context of finance and econometrics we construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive ou processes and we study these models in relation to financial data and theory

estimation of continuous time markov processes sampled at random time intervals we introduce a family of generalized method of moments estimators of the parameters of a continuous time markov process observed at random time intervals the results include strong consistency asymptotic normality and a characterization of standard errors sampling is at an arrival intensity that is allowed to depend on the underlying markov process and on the parameter vector to be estimated we focus on financial applications including tick based sampling allowing for jump diffusions regime switching diffusions and reflected diffusions

convergence of a discretization scheme for jump diffusion processes with state dependent intensities this paper proves a convergence result for a discretization scheme for simulating jump diffusion processes with state dependent jump intensities with a bound on the intensity the point process of jump times can be constructed by thinning a poisson random measure using state dependent thinning probabilities between the jump epochs of the poisson random measure the dynamics of the constructed process are purely diffusive and may be simulated using standard discretization methods under conditions on the coefficient functions of the jump diffusion process we show that the weak convergence order of this method equals the weak convergence order of the scheme used for the purely diffusive intervals the construction of jumps does not degrade the convergence of the method

new algorithms for solving periodic tridiagonal and periodic pentadiagonal linear systems abstract recently an efficient computational algorithm for solving periodic pentadiagonal linear systems has been proposed by karawia a a karawia a computational algorithm for solving periodic pentadiagonal linear systems appl math comput 174 2006 613 618 the algorithm is based on the lu factorization of the periodic pentadiagonal matrix in this paper new algorithms are presented for solving periodic pentadiagonal linear systems based on the use of any pentadiagonal linear solver in addition an efficient way of evaluating the determinant of a periodic pentadiagonal matrix is discussed the corresponding results in this paper can be readily obtained for solving periodic tridiagonal linear systems

synchronization based approach for parameters identification in delayed chaotic neural networks abstract in this paper an adaptive procedure to the problem of synchronization and parameters identification for chaotic neural networks with time varying delay is introduced by combining the adaptive control and linear feedback with appropriate update law based on the invariance principle of functional differential equations all the connection weight matrices can be efficiently estimated according to a simple rigorous and systematic technique this approach is also able to track the changes in the operating parameters of the experimental neural networks rapidly the speed of synchronization and parameters estimation can be adjusted under the adaptive gain properly chosen in addition the method is simple to implement in practice and it is quite robust against the effect of slight noise in the given time series and the estimated value of a parameter fluctuates around the correct value

analysis of a general stochastic non autonomous logistic model with delays and levy jumps abstract in this paper a general stochastic non autonomous logistic model with delays and levy jumps is proposed and studied sufficient criteria for extinction non persistence in the mean and weak persistence of the model are established the threshold between weak persistence and extinction is also obtained finally numerical simulations are introduced to illustrate the theoretical analysis results our results illustrate that both persistence and extinction have close relationships with time dependent delay and levy noise