propagation separation approach for local likelihood estimation the paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models including e g the regression density poisson and binary response model the method extends the adaptive weights smoothing aws procedure introduced in polzehl and spokoiny 2000 in context of image denoising the main idea of the method is to describe a greatest possible local neighborhood of every design point x i in which the local parametric assumption is justified by the data the method is especially powerful for model functions having large homogeneous regions and sharp discontinuities the performance of the proposed procedure is illustrated by numerical examples for density estimation and classification we also establish some remarkable theoretical nonasymptotic results on properties of the new algorithm this includes the propagation property which particularly yields the root n consistency of the resulting estimate in the homogeneous case we also state an oracle result which implies rate optimality of the estimate under usual smoothness conditions and a separation result which explains the sensitivity of the method to structural changes

on the spanning property of risk bonds priced by equilibrium we propose a method of pricing financial securities written on nontradable underlyings such as temperature or precipitation levels to this end we analyze a financial market where agents are exposed to financial and nonfinancial risk factors the agents hedge their financial risk in the stock market and trade a risk bond issued by an insurance company from the issuer s point of view the bond s primary purpose is to shift insurance risks related to noncatastrophic weather events to financial markets as such its terminal payoff and yield curve depend on an underlying climate or temperature process whose dynamics are independent of the randomness driving stock prices we prove that if the bond s payoff function is monotone in the external risk process it can be priced by an equilibrium approach the equilibrium market price of climate risk and the equilibrium price process are characterized as solutions of nonlinear backward stochastic differential equations bsdes transferring the bsdes into partial differential equations pdes we represent the bond prices as smooth functions of the underlying risk factors our analytical results make the model amenable to a numerical analysis

a direct method for constructing the traveling wave solutions of a modified generalized vakhnenko equation abstract proposing a direct method namely the traveling wave reduction combined with a smart variable transformation a series of traveling wave solutions are constructed for a modified generalized vakhnenko equation these solutions include the jacobi elliptic function solution the weierstrass elliptic function solution and the trigonometric function solution

the exponentiated weibull family a reanalysis of the bus motor failure data the weibull family with survival function exp y for 0 and y 0 is generalized by introducing an additional shape parameter the space of shape parameters 0 and 0 can be divided by boundary line 1 and curve 1 into four regions over which the hazard function is respectively increasing bathtub shaped decreasing and unimodal the new family is suitable for modeling data that indicate nonmonotone hazard rates and can be adopted for testing goodness of fit of weibull as a submodel the usefulness and flexibility of the family is illustrated by reanalyzing five classical data sets on bus motor failures from davis that are typical of data in repair reuse situations and efron s datapertainingtoahead and neck cancerclinical trial these illustrative datainvolvecensoring and indicate bathtub unimodal and increasing but possibly non weibull hazard shape models

the extended hyperbolic functions method and new exact solutions to the zakharov equations abstract the multiple exact solutions for the nonlinear evolution equations describing the interaction of laser plasma are developed the extended hyperbolic function method are employed to reveal these new solutions the solutions include that of the solitary wave solutions of bell type for n and e the solitary wave solutions of kink type for e and bell type for n the solitary wave solutions of a compound of the bell type and the kink type for n and e the singular traveling wave solutions periodic traveling wave solutions of triangle function types and solitary wave solutions of rational function types in addition to re deriving all known solutions in a systematic way several new and more general solutions can be obtained by using our method

periodic wave solutions and solitary wave solutions of generalized modified boussinesq equation and evolution relationship between both solutions abstract in this paper we focus on studying the exact solitary wave solutions and periodic wave solutions of the generalized modified boussinesq equation u t t u t t x x a 1 u a 2 u 2 a 3 u 3 x x 0 as well as the evolution relationship between these solutions detailed qualitative analysis is conducted on traveling wave solutions of this equation and global phase portraits in various parameter conditions are proposed various significant results about the existence of both solutions including three forms of solitary wave solutions and four exact bounded periodic wave solutions in different conditions are obtained then we further discuss the relationship between energy of hamiltonian system corresponding to this equation and the periodic wave solutions and solitary wave solutions it is concluded that the essential reason of periodic wave solutions and solitary wave solutions is the different values for the energy of hamiltonian system corresponding to this equation in addition the limited relations of periodic wave solutions and solitary wave solutions with the energy of hamiltonian system are proposed and the schematic diagram of evolution from periodic wave solutions to solitary wave solutions is drawn

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

systems of ordinary differential equations with nonlinear superposition principles abstract this work is concerned with the derivation of superposition rules which express the general solution of ordinary differential equations x x t x r n t r in terms of a finite number of particular solutions the point of departure is lie s criterion according to which such a rule exists if and only if the vector fields x t generate a finite dimensional lie algebra we provide three different constructive methods for deriving superposition rules and apply them to systems of coupled riccati equations of the projective and conformal types based respectively on the lie algebra sl n 1 r and o p 1 n p 1

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

weather forecasting for weather derivatives we take a simple time series approach to modeling and forecasting daily average temperature in u s cities and we inquire systematically as to whether it may prove useful from the vantage point of participants in the weather derivatives market the answer is perhaps surprisingly yes time series modeling reveals conditional mean dynamics and crucially strong conditional variance dynamics in daily average temperature and it reveals sharp differences between the distribution of temperature and the distribution of temperature surprises as we argue it also holds promise for producing the long horizon predictive densities crucial for pricing weather derivatives so that additional inquiry into time series weather forecasting methods will likely prove useful in weather derivatives contexts

methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order abstract in this paper we present several methods of judging shape of the solitary wave and solution formulae for some nonlinear evolution equations by means of lienard equations then using the judgement methods and solution formulae we obtain solutions of the solitary wave for some of important nonlinear evolution equations which include generalized modified boussinesq generalized nonlinear wave generalized fisher generalized klein gordon and generalized zakharov equations some new solitary wave solutions are found for the equations

on the integrability of systems of nonlinear ordinary differential equations with superposition principles a new class of solvable nonlinear dynamical systems has been recently identified by the requirement that the ordinary differential equations ode s describing each member of this class possess nonlinear superposition principles these systems of ode s are generally not derived from a hamiltonian and are classified by associated pairs of lie algebras of vector fields in this paper all such systems of n 3 ode s are integrated in a unified way by finding explicit integrals for them and relating them all to a pivotal member of their class the projective riccati equations moreover by perturbing two parametrically driven projective riccati equations thus making them nonsolvable in the above sense evidence is discovered of chaotic behavior on the poincare surface of section in the form of sensitive dependence on initial conditions near a boundary separating bounded from unbounded motion

explicit exact solutions for the generalized zakharov equations with nonlinear terms of any order in this paper an auxiliary ordinary differential equation with nonlinear terms of any order is introduced and its exact solutions are obtained by means of the auxiliary equation and its solutions abundant explicit exact solutions to the generalized zakharov equations with nonlinear terms of any order are obtained in a concise manner that include new solitary wave solutions and triangular periodic wave solutions

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

a new class of exact solutions for coupled scalar field equations the authors report a class of exact solutions valid in new regimes of parameter values for a generic system of nonlinear coupled scalar field equations which is the stationary reduction of the schrodinger boussinesq or korteweg de vries system and which extends the henon heiles system to hamiltonians with indefinite kinetic energy the results are applied to co propagating coupled nonlinear waves in magnetized plasmas

multiscale local change point detection with applications to value at risk this paper offers a new approach to modeling and forecasting of non stationary time series with applications to volatility modeling for financial data the approach is based on the assumption of local homogeneity for every time point there exists a historical interval of homogerzeity in which the volatility parameter can be well approximated by a constant the proposed procedure recovers this interval from the data using the local change point lcp analysis afterward the estimate of the volatility can be simply obtained by local averaging the approach carefully addresses the question of choosing the tuning parameters of the procedure using the so called propagation condition the main result claims a new oracle inequality in terms of the modeling bias which measures the quality of the local constant approximation this result yields the optimal rate of estimation for smooth and piecewise constant volatility functions then the new procedure is applied to some data sets and a comparison with a standard garch model is also provided finally we discuss applications of the new method to the value at risk problem the numerical results demonstrate a very reasonable performance of the new method

new exact traveling wave solutions for the klein gordon zakharov equations based on the extended hyperbolic functions method we obtain the multiple exact explicit solutions of the klein gordon zakharov equations the solutions obtained in this paper include a the solitary wave solutions of bell type for u and n b the solitary wave solutions of kink type for u and bell type for n c the solitary wave solutions of a compound of the bell type and the kink type for u and n d the singular traveling wave solutions e periodic traveling wave solutions of triangle function types and solitary wave solutions of rational function types we not only rederive all known solutions of the klein gordon zakharov equations in a systematic way but also obtain several entirely new and more general solutions the variety of structures of the exact solutions of the klein gordon zakharov equations is illustrated

localising temperature risk abstracton the temperature derivative market modeling temperature volatility is an important issue for pricing and hedging to apply the pricing tools of financial mathematics one needs to isolate a gaussian risk factor a conventional model for temperature dynamics is a stochastic model with seasonality and intertemporal autocorrelation empirical work based on seasonality and autocorrelation correction reveals that the obtained residuals are heteroscedastic with a periodic pattern the object of this research is to estimate this heteroscedastic function so that after scale normalization a pure standardized gaussian variable appears earlier works investigated temperature risk in different locations and showed that neither parametric component functions nor a local linear smoother with constant smoothing parameter are flexible enough to generally describe the variance process well therefore we consider a local adaptive modeling approach to find at each time point an optimal smoothing parameter to

traveling wave solutions for nonlinear equations using symbolic computation abstract in this paper a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations pdes is presented and implemented in a computer algebraic system the key idea of this method is to take full advantage of a riccati equation involving a parameter and use its solutions to replace the tanh function in the tanh method it is quite interesting that the sign of the parameter can be used to exactly judge the number and types of such travelling wave solutions in this way we can successfully recover the previously known solitary wave solutions that had been found by the tanh method and other more sophisticated methods more importantly for some equations with no extra effect we also find other new and more general solutions at the same time by introducing appropriate transformations our method is further extended to the nonlinear pdes whose balancing numbers may be any nonzero real numbers the efficiency of the method can be demonstrated on a large variety of nonlinear pdes such as those considered in this paper burgers huxley equation coupled korteweg de vries equation caudrey dodd gibbon kawada equation active dissipative dispersive media equation generalized fisher equation and nonlinear heat conduction equation

time varying periodicity in intraday volatility abstractwe develop a nonparametric test for whether return volatility exhibits time varying intraday periodicity using a long time series of high frequency data our null hypothesis commonly adopt

an implementation of the adm for generalized one dimensional klein gordon equation in this study a decomposition method for approximating the solution of the generalized one dimensional klein gordon equation is implemented to illustrate the application of this method numerical results are derived by using the calculated components of the decomposition series the obtained results are found to be in good agreement with the exact solution

a simple bootstrap method for constructing nonparametric confidence bands for functions standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators to overcome this problem it is common practice to either undersmooth so as to reduce the impact of bias or oversmooth and thereby introduce an explicit or implicit bias estimator however these approaches and others based on nonstandard smoothing methods complicate the process of inference for example by requiring the choice of new unconventional smoothing parameters and in the case of undersmoothing producing relatively wide bands in this paper we suggest a new approach which exploits to our advantage one of the difficulties that in the past has prevented an attractive solution to the problem the fact that the standard bootstrap bias estimator suffers from relatively high frequency stochastic error the high frequency together with a technique based on quantiles can be exploited to dampen down the stochastic error term leading to relatively narrow simple to construct confidence bands

note on exact solutions for a class of nonlinear diffusion equations an effective characterization is given for a class of generalized nonlinear diffusion equations with power law dependent terms further a new auxiliary equation ansatz is derived consequently new exact traveling wave trigonometric function solitary like and weierstrass elliptic solutions to a subclass are obtained by means of an auxiliary equation method and a generalized riccati equation expansion method

exact travelling wave solutions of nonlinear evolution equations in 1 1 and 2 1 dimensions abstract based upon the symbolic computation system maple the projective riccati equation method is improved to seek for travelling wave solutions in 1 1 and 2 1 dimensional nonlinear evolution equations by introducing two new elementary bell shaped and kink shaped functions the validity and reliability of the method is tested by applying it to the 2 1 dimensional generalized of the shallow water wave equation potential kdv equation and burgers kdv equation

explicit wave front solutions of noyes field systems for the belousov zhabotinskii reaction abstract in this paper four kinds of explicit traveling wave front solutions of a simplified noyes field model for the belousov zhabotinskii reaction b z reaction i e the reaction diffusion system formula are obtained they are useful for a better understanding of the b z reaction and the methods used here might also be useful for finding explicit traveling wave front solutions of mathematical models in other fields such as in physics biology and engineering

new exact travelling wave solutions of two nonlinear physical models abstract in this paper an improved tanh function method is used with a computerized symbolic computation for constructing new exact travelling wave solutions on two nonlinear physical models namely the quantum zakharov equations and the 2 1 dimensional broer kaup kupershmidt bkk system the main idea of this method is to take full advantage of the riccati equation which has more new solutions the exact solutions are obtained which include new soliton like solutions trigonometric function solutions and rational solutions the method is straightforward and concise and its applications are promising

a series of abundant exact travelling wave solutions for a modified generalized vakhnenko equation using auxiliary equation method in this paper a series of abundant exact travelling wave solutions is established for a modified generalized vakhnenko equation by using auxiliary equation method these solutions can be expressed by jacobi elliptic function when jacobi elliptic functions modulus m 1 or 0 the travelling wave solutions degenerate to four types of solutions namely the soliton solutions the hyperbolic function solutions the trigonometric function solutions constant solutions

statistical inference of reliability of generalized rayleigh distribution under progressively type ii censoring abstract generalized rayleigh distribution is an important continuous life distribution which plays a key role in reliability engineering research in this paper the statistical inference of reliability of generalized rayleigh distribution is studied based on the progressively type ii censored data first we obtain the estimates through maximum likelihood estimation and by using bootstrap methods boot p and boot t we estimate the confidence intervals of parameters and reliability in addition based on the square error loss function the bayes estimation of the reliability function is carried out by adopting the gibbs sampling method and the point estimation the highest posterior density h p d confidence interval estimation are carried out respectively a numerical simulation and an authentic example are used to illustrate the proposed inference methods finally the approximate estimation of stress strength reliability is further studied

backlund transformation lax pairs and explicit exact solutions for the shallow water waves equation in this paper we consider the hirota satsuma equation for shallow water waves we first obtain the backlund transformation and lax pairs by using the extended homogeneous balance method then we find some explicit exact solutions by means of backlund transformation and the extended hyperbolic function method these solutions include the solitary wave solution of rational function soliton solutions double soliton solutions n soliton solutions the multiple solitary wave solutions singular solutions and the periodic wave solutions of triangle function type

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave