mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

global behavior of positive solutions of nonlinear three point boundary value problems we investigate the structure of the positive solution set for nonlinear three point boundary value problems of the form u h t f u 0 u 0 0 u 1 lambdau eta where eta epsilon 0 1 is given lambda epsilon 0 1 n is a parameter f epsilon c 0 infinity 0 infinity satisfies f s 0 for s 0 and h epsilon c 0 1 0 infinity is not identically zero on any subinterval of 0 1 our main results demonstrate the existence of continua of positive solutions of the above problem c 2004 elsevier ltd all rights reserved

existence results for semilinear differential equations with nonlocal and impulsive conditions abstract this paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions using the techniques of approximate solutions and fixed point existence results are obtained for mild solutions when the impulsive functions are only continuous and the nonlocal item is lipschitz in the space of piecewise continuous functions is not lipschitz and not compact is continuous in the space of bochner integrable functions respectively

point process modelling for directed interaction networks abstract network data often take the form of repeated interactions between senders and receivers tabulated over time a primary question to ask of such data is which traits and behaviors are predictive of interaction to answer this question a model is introduced for treating directed interactions as a multivariate point process a cox multiplicative intensity model using covariates that depend on the history of the process consistency and asymptotic normality are proved for the resulting partial likelihood based estimators under suitable regularity conditions and an efficient fitting procedure is described multicast interactions those involving a single sender but multiple receivers are treated explicitly the resulting inferential framework is then employed to model message sending behavior in a corporate e mail network the analysis gives a precise quantification of which static shared traits and dynamic network effects are predictive of message recipient selection

regular problem for solutions of a retarded semilinear differential nonlocal equation abstract this paper deals with the regularity and existence of solutions of a retarded semilinear differential equation with nonlocal condition by using the fundamental solution in the case where the principal operators are unbounded operators

controllability of fractional integro differential evolution equations with nonlocal conditions this paper concerns the controllability for a class of fractional integro differential evolution equations with nonlocal initial conditions by using the fractional calculus measure of noncompactness and the monch fixed point theorem we obtain a controllability result for the nonlocal cauchy problem of the fractional integro differential evolution equations involving noncompact semigroups and the nonlocal functions without lipschitz continuity an example is given to illustrate the effectiveness of the abstract results

existence of solutions for semilinear neutral stochastic functional differential equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii fixed point theorem the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions is studied the results are a generalization and continuation of the recent results on this issue an example is provided to illustrate the theory

statistical clustering of temporal networks through a dynamic stochastic block model statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges here we explore statistical properties and frequentist inference in a model that combines a stochastic block model sbm for its static part with independent markov chains for the evolution of the nodes groups through time we model binary data as well as weighted dynamic random graphs with discrete or continuous edges values our approach motivated by the importance of controlling for label switching issues across the different time steps focuses on detecting groups characterized by a stable within group connectivity behavior we study identifiability of the model parameters propose an inference procedure based on a variational expectation maximization algorithm as well as a model selection criterion to select for the number of groups we carefully discuss our initialization strategy which plays an important role in the method and compare our procedure with existing ones on synthetic datasets we also illustrate our approach on dynamic contact networks one of encounters among high school students and two others on animal interactions an implementation of the method is available as a r package called dynsbm

existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense given by grimmer in r grimmer resolvent operators for integral equations in a banach space transaction of american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of the strict solutions

controllability for a class of integro differential evolution equations involving non local initial conditions abstractthis paper deals with the exact controllability for a class of first order integro differential evolution equations involving non local initial conditions by using sadovskii fixed point theorem exact controllability results are obtained without assuming the compactness and lipschitz conditions for non local functions an example is given to illustrate the effectiveness of the abstract results

fractional martingales and characterization of the fractional brownian motion in this paper we introduce the notion of fractional martingale as the fractional derivative of order of a continuous local martingale where 1 2 1 2 and we show that it has a nonzero finite variation of order 2 1 2 under some integrability assumptions on the quadratic variation of the local martingale as an application we establish an extension of levy s characterization theorem for the fractional brownian motion

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

on a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general banach spaces abstract sufficient conditions on the existence of mild solutions for the following semilinear nonlocal evolution inclusion with upper semicontinuous nonlinearity u t a t u t f t u t 0 t d u 0 g u are given when g is completely continuous and lipschitz continuous in general banach spaces respectively an example concerning the partial differential equation is also presented

on nested infinite occupancy scheme in random environment we consider an infinite balls in boxes occupancy scheme with boxes organised in nested hierarchy and random probabilities of boxes defined in terms of iterated fragmentation of a unit mass we obtain a multivariate functional limit theorem for the cumulative occupancy counts as the number of balls approaches infinity in the case of fragmentation driven by a homogeneous residual allocation model our result generalises the functional central limit theorem for the block counts in ewens and more general regenerative partitions

existence of nondensely defined evolution equations with nonlocal conditions abstract this paper is concerned with the existence for nondensely defined evolution equations with nonlocal conditions using the techniques of fixed point theory and approximate solutions existence results are obtained for integral solutions when the nonlocal item is lipschitz continuous or continuous respectively examples are also given to illustrate our results

assessing a mixture model for clustering with the integrated completed likelihood we propose an assessing method of mixture model in a cluster analysis setting with integrated completed likelihood for this purpose the observed data are assigned to unknown clusters using a maximum a posteriori operator then the integrated completed likelihood icl is approximated using the bayesian information criterion bic numerical experiments on simulated and real data of the resulting icl criterion show that it performs well both for choosing a mixture model and a relevant number of clusters in particular icl appears to be more robust than bic to violation of some of the mixture model assumptions and it can select a number of dusters leading to a sensible partitioning of the data

a unified existence theory for evolution equations and systems under nonlocal conditions abstract we investigate the effect of nonlocal conditions expressed by linear continuous mappings over the hypotheses which guarantee the existence of global mild solutions for functional differential equations in a banach space a progressive transition from the volterra integral operator associated to the cauchy problem to fredholm type operators appears when the support of the nonlocal condition increases from zero to the entire interval of the problem the results are extended to systems of equations in a such way that the system nonlinearities behave independently as much as possible and the support of the nonlocal condition may differ from one variable to another

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators in this paper by using the leray schauder alternative we have investigated the existence of mild solutions to first order impulsive partial functional integrodifferential equations with nonlocal conditions in an a norm we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a lipschitz continuous function with respect to the fractional power norm of the linear part an example is also given to illustrate our main results

a semiparametric extension of the stochastic block model for longitudinal networks we propose an extension of the stochastic block model for recurrent interaction events in continuous time where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous poisson process with intensity driven by the individuals latent groups we show that the model is identifiable and estimate it with a semiparametric variational expectation maximization algorithm we develop two versions of the method one using a nonparametric histogram approach with an adaptive choice of the partition size and the other using kernel intensity estimators we select the number of latent groups by an integrated classification likelihood criterion we demonstrate the performance of our procedure on synthetic experiments analyse two datasets to illustrate the utility of our approach and comment on competing methods

partial approximate controllability of nonlocal fractional evolution equations via approximating method abstract in this paper we study partial approximate controllability of semilinear nonlocal fractional evolution equations in hilbert spaces by using fractional calculus variational approach and approximating technique we give the approximate problem of the control system and get the compactness of approximate solution set then new sufficient conditions for the partial approximate controllability of the control system are obtained when the compactness conditions or lipschitz conditions for the nonlocal function are not required finally we apply our abstract results to the partial approximate controllability of the semilinear heat equation and delay equation

approximate controllability of semilinear evolution equations of fractional order with nonlocal and impulsive conditions via an approximating technique abstract this paper is concerned with the approximate controllability of the semilinear fractional evolution equations with nonlocal and impulsive conditions our main results are obtained by utilizing the technique of approximate solution and the theory of fixed point in addition the impulsive functions in this paper are supposed to be continuous and the nonlocal item is divided into two cases lipschitz continuous and only continuous which generalizes the previous contributions finally two examples are worked out to illustrate our obtained results

existence results for impulsive differential inclusions with nonlocal conditions abstract in this paper we shall establish sufficient conditions for the existence of mild solutions for nonlocal impulsive differential inclusions on the basis of the fixed point theorems for multivalued maps and the technique of approximate solutions new results are obtained examples are also provided to illustrate our results

an extension of the levy characterization to fractional brownian motion assume that x is a continuous square integrable process with zero mean defined on some probability space f p the classical characterization due to p levy says that x is a brownian motion if and only if x and x 2 t t t 0 are martingales with respect to the intrinsic filtration f x we extend this result to fractional brownian motion

existence results for systems with coupled nonlocal initial conditions abstract in this paper an existence theory is developed for first order differential systems with coupled nonlocal conditions given by stieltjes integrals the approach is based on the fixed point theorems of perov schauder and schaefer and on a vector method for treating systems which uses matrices having spectral radius less than one when the nonlocal conditions depend on functionals restricted to a proper subinterval the nonlinear integral operator associated to the system splits into two parts one of fredholm type and another one of volterra type correspondingly the sufficient conditions for the existence results will differ in the two parts of the interval some examples are presented to illustrate the theory

intermittency for the stochastic heat equation driven by a rough time fractional gaussian noise this paper studies the stochastic heat equation driven by time fractional gaussian noise with hurst parameter h in 0 1 2 we establish the feynman kac representation of the solution and use this representation to obtain matching lower and upper bounds for the l p omega moments of the solution

existence of mild solutions for the semilinear nonlocal problem in banach spaces abstract in this paper we study the existence of mild solutions of the semilinear nonlocal initial value problem on a bounded and on an unbounded interval in our considerations we apply a new calculation method based on the technique of modulus of continuity in conjunction with idea of the family of measures of noncompactness in frechet space the results obtained in this paper generalize several ones obtained earlier by many authors

nonlocal differential equations with multivalued perturbations in banach spaces abstract we discuss the existence of mild solutions for nonlocal differential inclusions with multivalued perturbations in banach spaces and establish new existence theorems for related cauchy problems which extend some existing results in this area using the established results we investigate a special nonlocal problem finally we also consider a partial functional differential equation

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

nonlocal nonlinear differential equations with a measure of noncompactness in banach spaces abstract in this paper we give the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions under the assumptions of the hausdorff measure of noncompactness in separable and uniformly smooth banach spaces

on the existence and asymptotic behaviour of solutions of an evolution equation and an application to the feynman kac theorem abstract in this paper we study the existence of mild solutions of a semilinear evolution equation on an unbounded interval the rapidity of the growth of those solutions is characterized moreover we investigate the local and global attractivity of solutions of an equation in question and we describe their asymptotic behaviour our investigations are conducted in a real separable banach space

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

nonlocal in time problem for anisotropic parabolic equations with variable exponents of nonlinearities abstract in this study we consider nonlinear parabolic equations with variable exponents of the nonlinearities the nonlocal problem for these equations is investigated and the existence and uniqueness theorems are proved for the problem

existence of classical solutions to nonautonomous nonlocal parabolic problems abstract we obtain a new existence theorem for classical solutions to nonautonomous equations with nonlocal initial conditions u t a t u t f t u t t s t u s g u u 0 in a banach space x where t s 0 f g are given x valued functions and a t is a sectorial operator not necessarily densely defined in x for each t 0 t both banach s contraction principle and schauder s fixed point theorem as well as the theory of evolution families and interpolation spaces are employed in our approach a concrete example is shown to illustrate the existence theorem

on a class of retarded integro differential equations with nonlocal initial conditions of concern is the following cauchy problem for fractional integro differential equations with time delay and nonlocal initial condition u t email protected 0 t t s m email protected m 1 au s ds f t u t u k t t 0 u t h t u email protected t email protected email protected 0 where 1 0 a d a x x is a generator of a solution operator on a complex banach space x the convolution integral in the equation is known as the riemann liouville fractional integral k t 0 email protected representing the delay property is a function and h t is an operator defined from email protected 0 xc email protected 0 x into x for some t 0 which constitutes a nonlocal condition the local existence and uniqueness of mild solutions for the cauchy problem under various criteria are proved moreover we present an existence result of the global solution also an example is given to illustrate the applications of the abstract results

controllability of impulsive differential systems with nonlocal conditions abstract the paper is concerned with the controllability of impulsive functional differential equations with nonlocal conditions using the measure of noncompactness and monch fixed point theorem we establish some sufficient conditions for controllability firstly we require the equicontinuity of evolution system and next we only suppose that the evolution system is strongly continuous since we do not assume that the evolution system generates a compact semigroup our theorems extend some analogous results of impulsive control systems

existence for a class of partial differential equations with nonlocal conditions abstract this paper is concerned with the existence of mild and classical solutions of nonlocal cauchy problems we assume that the linear part generates an analytic compact bounded semigroup and that the nonlinear part is a holder continuous function with respect to the fractional power norm of the linear part considering the nonlocal conditions in the norm we generalize the recent conclusions on this topic the results obtained will be applied to a class of functional partial differential equations with nonlocal conditions in 1 2 norm

approximate controllability results for non densely defined fractional neutral differential inclusions with hille yosida operators abstractin this paper we mainly focused the approximate controllability results for a class of non densely defined fractional neutral differential control systems first we establish a set of suf

identifiability of parameters in latent structure models with many observed variables while hidden class models of various types arise in many statistical applications it is often difficult to establish the identifiability of their parameters focusing on models in which there is some structure of independence of some of the observed variables conditioned on hidden ones we demonstrate a general approach for establishing identifiability utilizing algebraic arguments a theorem of j kruskal for a simple latent class model with finite state space lies at the core of our results though we apply it to a diverse set of models these include mixtures of both finite and nonparametric product distributions hidden markov models and random graph mixture models and lead to a number of new results and improvements to old ones in the parametric setting this approach indicates that for such models the classical definition of identifiability is typically too strong instead generic identifiability holds which implies that the set of nonidentifiable parameters has measure zero so that parameter inference is still meaningful in particular this sheds light on the properties of finite mixtures of bernoulli products which have been used for decades despite being known to have nonidentifiable parameters in the nonparametric setting we again obtain identifiability only when certain restrictions are placed on the distributions that are mixed but we explicitly describe the conditions

impulsive problems for semilinear differential equations with nonlocal conditions abstract this paper is concerned with the existence of impulsive semilinear differential equations with nonlocal conditions using the technique of fixed point theory existence results are obtained for mild solutions when the nonlocal item is lipschitz is not lipschitz and not compact respectively

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

nonlocal solutions of parabolic equations with strongly elliptic differential operators abstract the paper deals with second order parabolic equations on bounded domains with dirichlet conditions in arbitrary euclidean spaces their interest comes from being models for describing reaction diffusion processes in several frameworks a linear diffusion term in divergence form is included which generates a strongly elliptic differential operator a further linear part of integral type is present which accounts of nonlocal diffusion behaviours the main result provides a unifying method for studying the existence and localization of solutions satisfying nonlocal associated boundary conditions the cauchy multipoint and the mean value conditions are included in this investigation the problem is transformed into its abstract setting and the proofs are based on the homotopic invariance of the leray schauder topological degree a bounding function i e lyapunov like function theory is developed which is new in this infinite dimensional context it allows that the associated vector fields have no fixed points on the boundary of their domains and then it makes possible the use of a degree argument

existence of solutions for neutral functional differential evolution equations with nonlocal conditions abstract in this paper by using fractional power of operators and sadovskii s fixed point theorem we study the existence of mild and strong solutions of semilinear neutral functional differential evolution equations with nonlocal conditions the results we obtained are a generalization and continuation of the recent results on this issue in the end an example is given to show the application of our results

existence results of semilinear differential equations with nonlocal initial conditions in banach spaces abstract in this paper we establish the existence results for semilinear differential systems with nonlocal initial conditions in banach spaces the approaches used are fixed point theorems combined with convex power condensing operators the first result obtained will be applied to a class of semilinear parabolic equations

estimating the intensity of a random measure by histogram type estimators the purpose of this paper is to estimate the intensity of some random measure n on a set mathcal x by a piecewise constant function on a finite partition of mathcal x given a possibly large family mathcal m of candidate partitions we build a piecewise constant estimator histogram on each of them and then use the data to select one estimator in the family choosing the square of a hellinger type distance as our loss function we show that each estimator built on a given partition satisfies an analogue of the classical squared bias plus variance risk bound moreover the selection procedure leads to a final estimator satisfying some oracle type inequality with as usual a possible loss corresponding to the complexity of the family mathcal m when this complexity is not too high the selected estimator has a risk bounded up to a universal constant by the smallest risk bound obtained for the estimators in the family for suitable choices of the family of partitions we deduce uniform risk bounds over various classes of intensities our approach applies to the estimation of the intensity of an inhomogenous poisson process among other counting processes or the estimation of the mean of a random vector with nonnegative components

a note on riemann liouville processes abstract in this note it is proved that under certain conditions riemann liouville processes can arise from the temporal structures of the functional fluctuation limits of the occupation times of a type of spatial inhomogeneous branching particle system with infinite variances

mild solutions of semilinear evolution equation on an unbounded interval and their applications the aim of this paper is to give an existence theorem for a semilinear equation of evolution on an unbounded interval in the case when the generator of a semigroup depends on time parameter the considerations of this paper are based on the concept of a measure of noncompactness in frechet space and the classical tichonov fixed point principle moreover an application of the main theorem to the second order parabolic pde is given

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

existence and asymptotic properties of solutions of nonlinear multivalued differential inclusions with nonlocal conditions abstract this paper deals with a nonlocal problem governed by the nonlinear differential inclusions with multivalued perturbations in banach spaces first using the approach of geometry of banach space hausdorff metric the measure of noncompactness and fixed point existence results are obtained we have removed from previous papers the crucial restriction on the semigroup then we establish the asymptotic properties of integral solutions when t finally for illustration a partial differential equation is worked out

nonlocal cauchy problems for neutral functional differential and integrodifferential inclusions in banach spaces in this paper we investigate the existence of mild solutions on a compact interval to initial value problems for neutral functional differential and integrodifferential inclusions in banach spaces with nonlocal conditions the results are obtained by using a fixed point theorem for condensing maps due to martelli

uniqueness of solutions of parabolic semilinear nonlocal boundary problems abstract the purpose of the paper is to give two theorems about the uniqueness of solutions of parabolic semilinear nonlocal boundary problems the paper is a continuation of previous papers by byszewski and the generalization of some results from r rabczuk introduction to differential inequalities pwn warsaw 1976 polish j chabrowski on nonlocal problems for parabolic equations nagoya math j 93 1984 109 131 the theorems obtained in this paper can be applied in the theories of diffusion and heat conduction with better effects than the analogous theorems about parabolic initial boundary problems and than the analogous theorems about parabolic periodic boundary problems