risk sensitive and risk neutral multiarmed bandits for the multiarmed bandit the classic result is probabilistic each state of each bandit markov chain with rewards has an index that is determined by an optimal stopping time for that state s bandit and expected discounted income is maximized by playing at each epoch a bandit whose current state has the largest index our approach is analytic not probabilistic it uses pairwise comparison in place of stopping times a simple recursion assigns to each state of each bandit a utility and an amplification of future utility that depend solely on the data for that state s bandit these utilities and amplifications determine whether or not one state dominates another we show that it is optimal to play at each epoch any bandit whose current state is not dominated by the current states of the other bandits we obtain this result by a coherent analysis that encompasses three models one with risk averse exponential utility one with risk seeking exponential utility and one with linear utility and either stopping or discounting we also show that the risk seeking case and a model of nash nash p 1980 a generalized bandit problem j roy statist soc b42 165 169 are equivalent to each other

perturbations of elliptic operators in 1 sided chord arc domains part i small and large perturbation for symmetric operators the first and third authors acknowledge financial support from the spanish ministry of economy and competitiveness through the severo ochoa programme for centres of excellence in r d sev 2015 0554 they also acknowledge that the research leading to these results has received funding from the european research council under the european union s seventh framework programme fp7 2007 2013 erc agreement no 615112 hapdegmt the second author was supported by nsf grant dms 1664047

degradation in common dynamic environments abstractdegradation studies are often used to assess reliability of products subject to degradation induced soft failures because of limited test resources several test subjects may have to share a test rig and have their degradation measured by the same operator the common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation which is known as the block effect in the present article the wiener process is used to model product degradation and the group specific random environments are captured using a stochastic time scale both semiparametric and parametric estimation procedures are developed for the model maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the em algorithm performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations the proposed models are illustrated by an appl

hausdorff content and the hardy littlewood maximal operator on metric measure spaces abstract let x d be a complete metric measure space and be a non negative borel regular measure satisfying the doubling condition with some dimensional constant d we prove that the hausdorff content of codimension 0 denoted by h and the hardy littlewood maximal operator m satisfy the strong type inequality x m u p d h c x u p d h 0 u l loc 1 x whenever p max 0 1 d if further satisfies some reverse doubling condition with some other dimensional constant then for the endpoint case p 1 d with 0 d 0 we also obtain the corresponding weak type estimate for h and m the fundamental point in the proofs is to introduce and develop a theory of the dyadic hausdorff content h d which is a choquet capacity comparable to h and has the strong subadditivity property

harmonic measure and quantitative connectivity geometric characterization of the l p solvability of the dirichlet problem it is well known that quantitative scale invariant absolute continuity more precisely the weak a infty property of harmonic measure with respect to surface measure on the boundary of an open set omega subset mathbb r n 1 with ahlfors david regular boundary is equivalent to the solvability of the dirichlet problem in omega with data in l p partial omega for some p infty in this paper we give a geometric characterization of the weak a infty property of harmonic measure and hence of solvability of the l p dirichlet problem for some finite p this characterization is obtained under background hypotheses an interior corkscrew condition along with ahlfors david regularity of the boundary that are natural and in a certain sense optimal we provide counter examples in the absence of either of them or even one of the two upper or lower ahlfors david bounds moreover the examples show that the upper and lower ahlfors david bounds are each quantitatively sharp

duality of hardy and bmo spaces associated with operators with heat kernel bounds the introduction and development of hardy and bmo spaces on euclidean spaces r in the 1960s and 1970s played an important role in modern harmonic analysis and applications in partial differential equations these spaces were studied extensively in 32 22 18 19 31 and many others an l function f on r is in the hardy spaceh r if the area integral function of the poisson integral e t f satisfies

an inverse gaussian process model for degradation data this paper studies the maximum likelihood estimation of a class of inverse gaussian process models for degradation data both the subject to subject heterogeneity and covariate information can be incorporated into the model in a natural way the em algorithm is used to obtain the maximum likelihood estimators of the unknown parameters and the bootstrap is used to assess the variability of the maximum likelihood estimators simulations are used to validate the method the model is fitted to laser data and corresponding goodness of fit tests are carried out failure time distributions in terms of degradation level passages are calculated and illustrated the supplemental materials for this article are available online

optimum allocation rule for accelerated degradation tests with a class of exponential dispersion degradation models optimum allocation problem in accelerated degradation tests adts is an important task for reliability analysts several researchers have attempted to address this decision problem but their results have been based only on specific degradation models therefore they lack a unified approach toward general degradation models this study proposes a class of exponential dispersion ed degradation models to overcome this difficulty assuming that the underlying degradation path comes from the ed class we analytically derive the optimum allocation rules by minimizing the asymptotic variance of the estimated q quantile of product s lifetime for two level and three level adt allocation problems whether the testing stress levels are prefixed or not for a three level allocation problem we show that all test units should be allocated into two out of three stresses depending on certain specific conditions two examples are used to illustrate the proposed procedure furthermore the penalties of using nonopt

carleson measure problems for parabolic bergman spaces and homogeneous sobolev spaces abstract let b p r 1 n be the space of solutions to the parabolic equation t u u 0 0 1 having finite l p r 1 n norm we characterize nonnegative radon measures on r 1 n having the property u l q r 1 n u w 1 p r 1 n 1 p q whenever u t x b p r 1 n w 1 p r 1 n meanwhile denoting by v t x the solution of the above equation with cauchy data v 0 x we characterize nonnegative radon measures on r 1 n satisfying v t 2 x l q r 1 n v 0 w p r n 0 n p 1 n q 0 moreover we obtain the decay of v t x an isocapacitary inequality and a trace inequality

classes of carleson type measures generated by capacities we introduce classes of measures in the half space mathbb r n 1 generated by riesz or bessel or besov capacities in mathbb r n and give a geometric characterization of these as carleson type measures

index policies for stochastic search in a forest with an application to r d project management this paper concerns a stochastic search problem in a forest as motivation consider the issue of investing in a research and development project each activity that could be undertaken in the project is represented as an edge in a forest each edge has a cost of being attempted and a probability of success an edge can be attempted if each of its predecessors has been attempted and if each of those attempts has succeeded the overall project succeeds if a path is found from a stem to a leaf of the forest all of whose edges are successful overall success yields an economic benefit the problem is to find an investment strategy that maximizes expected utility either with a linear or an exponential utility function this problem will be shown to have a simple solution each edge will be assigned an index such that expected utility is maximized by attempting at each opportunity an edge whose index is most positive terminating the search when no edges remain whose indices are positive these indices are nested in a way that makes them quick to compute

well posedness of quasi geostrophic equations with data in besov q spaces abstract by wavelets and multi resolution analysis we convert the bilinear estimate on tent spaces associated with besov q spaces b p p 1 2 r n to the estimates of the numerical quantities as an application we get the well posedness of the quasi geostrophic equations with initial data in b p p 1 2 r 2

carleson embeddings for sobolev spaces via heat equation abstract let u t x be the solution of the heat equation t x u t x 0 on r 1 n 0 r n subject to u 0 x f x on r n the main goal of this paper is to characterize such a nonnegative measure on r 1 n that f x u t 2 x induces a bounded embedding from the sobolev space w 1 p r n p 1 n into the lebesgue space l q r 1 n q 0

strong type estimates for homogeneous besov capacities capacitary strong type estimates for homogeneous besov spaces are established moreover the result is used to study embeddings and dualities of function spaces

on the analyticity of the semigroup generated by the stokes operator with neumann type boundary conditions on lipschitz subdomains of riemannian manifolds we study the analyticity of the semigroup generated by the stokes operator equipped with neumann type boundary conditions on l p spaces in lipschitz domains our strategy is to regularize this operator by considering the hodge laplacian which has the additional property that it commutes with the leray projection

semigroup characterization of besov type morrey spaces and well posedness of generalized navier stokes equations abstract the well posedness of generalized navier stokes equations with initial data in some critical homogeneous besov spaces and in some critical q spaces was known in this paper we establish a wavelet characterization of besov type morrey spaces under the action of semigroup as an application we obtain the well posedness of smooth solution for the generalized navier stokes equations with initial data in some critical homogeneous besov type morrey spaces b p p 1 2 n 1 2 1 1 2 1 2 1 p 2 and n p 2 2 2 n p or 2 p and max n p 2 2 1 2 n p with divergence free these critical homogeneous besov type morrey spaces are larger than corresponding classical besov spaces and cover q spaces

square function non tangential maximal function estimates and the dirichlet problem for non symmetric elliptic operators a we consider divergence form elliptic operators l div a x defined in the half space rn 1 n 2 where the coefficient matrix a x is bounded measurable uniformly elliptic t independent and not necessarily symmetric we establish square function non tangential maximal function estimates for solutions of the homogeneous equation lu 0 and we then combine these estimates with the method of approximability to show that l harmonic measure is absolutely continuous with respect to surface measure i e n dimensional lebesgue measure on the boundary in a scale invariant sense more precisely that it belongs to the class a with respect to surface measure equivalently that the dirichlet problem is solvable with data in lp for some p previously these results had been known only in the case n 1

a john nirenberg type inequality for qα rn abstract the john nirenberg inequality characterizes functions in the space bmo in terms of the decay of the distribution function of their oscillations over a cube in this paper we prove separate necessary and sufficient john nirenberg type inequalities for functions in the space q r n introduced by essen janson peng and xiao who conjectured a version of this inequality our results are a modified version of their conjecture and we give a counterexample to show the necessity for this modification the counterexample also shows that these necessary and sufficient conditions cannot be reconciled

quadratic estimates and functional calculi of perturbed dirac operators we prove quadratic estimates for complex perturbations of dirac type operators and thereby show that such operators have a bounded functional calculus as an application we show that spectral projections of the hodge dirac operator on compact manifolds depend analytically on l changes in the metric we also recover a unified proof of many results in the calderon program including the kato square root problem and the boundedness of the cauchy operator on lipschitz curves and surfaces

characterizations of weighted besov and triebel lizorkin spaces via temperatures abstract hardy littlewood type characterizations via temperatures on a half space of weighted besov and triebel lizorkin spaces studied recently by the author are given in the proof of the sufficient parts of the results a sub mean value property of temperatures is used in an elegant way to get control of certain terms by the hardy maximal function or its vector valued version as a byproduct of the results another characterization of weighted hardy spaces as well as characterizations of the gauss weierstrass integrals on a strip domain of distributions in the above weighted spaces is obtained also

new applications of besov type and triebel lizorkin type spaces abstract in this paper the authors prove that besov morrey spaces are proper subspaces of besov type spaces b p q s r n and that triebel lizorkin morrey spaces are special cases of triebel lizorkin type spaces f p q s r n the authors also establish an equivalent characterization of b p q s r n when 0 1 p these besov type spaces b p q s r n and triebel lizorkin type spaces f p q s r n were recently introduced to connect besov spaces and triebel lizorkin spaces with q spaces moreover for the spaces b p q s r n and f p q s r n the authors investigate their trace properties and the boundedness of the pseudo differential operators with homogeneous symbols in these spaces which generalize the corresponding classical results of jawerth and grafakos torres by taking 0

numerical approximation of the integral fractional laplacian we propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional laplacian we first derive an integral representation of the bilinear form corresponding to the variational problem the numerical approximation of the action of the corresponding stiffness matrix consists of three steps 1 apply a sinc quadrature scheme to approximate the integral representation by a finite sum where each term involves the solution of an elliptic partial differential equation defined on the entire space 2 truncate each elliptic problem to a bounded domain 3 use the finite element method for the space approximation on each truncated domain the consistency error analysis for the three steps is discussed together with the numerical implementation of the entire algorithm the results of computations are given illustrating the error behavior in terms of the mesh size of the physical domain the domain truncation parameter and the quadrature spacing parameter

student t processes for degradation analysis stochastic processes are widely used to analyze degradation data and the gaussian process is a particularly common one in this article we propose a robust statistical model using a student t pro

the kato problem for operators with weighted ellipticity we consider second order operators lw w 1 divawr with ellipticity controlled by a muckemphout a2 weight w we prove that the kato square root estimate l 1 2 w f l2 w kr fkl2 w holds in the weighted space l 2 w

the solution of the kato problem for degenerate elliptic operators with gaussian bounds we prove the kato conjecture for degenerate elliptic operators on r n more precisely we consider the divergence form operator lw w 1 diva where w is a muckenhoupt a2 weight and a is a complex valued n n matrix such that w 1 a is bounded and uniformly elliptic we show that if the heat kernel of the associated semigroup e tlw satisfies gaussian bounds then the weighted kato square root estimate kl 1 2 w f k l2 w k f k l2 w holds

the solution of the kato problem for divergence form elliptic operators with gaussian heat kernel bounds which in turnhas applications to the perturbation theory for certain classes of hyperbolicequations see 16 we remark that 1 3 is equivalent to the oppositeinequality for the square root of the adjoint operator l in 13 14 kato conjectured that an abstract version of 1 3 might hold for regularly accretive operators see 14 18 for the details a counter example to this abstract conjecture was obtained by mcintosh 17 whothen reformulated the conjecture in the following form bearing in mind thatkato s interest in the problem had been motivated by the special case ofelliptic di erential operators conjecture 1 4 the estimate 1 3 holds for lde ned as in 1 2 for anyl

hausdorff besov type and triebel lizorkin type spaces and their applications abstract let s r p 1 and 0 1 p where p denotes the conjugate index of p in this article the authors first introduce the hausdorff besov type space b h p q s r n with q 1 and the hausdorff triebel lizorkin type space f h p q s r n with q 1 via a class of weights defined on the upper plane and then establish some equivalent characterizations of b h p q s r n and f h p q s r n via some classes of weights defined on r n the authors then prove that their dual spaces are besov morrey and triebel lizorkin morrey spaces respectively the relations between these spaces and the known besov triebel lizorkin hausdorff spaces are also studied as an application for p 1 and 0 n the authors obtain the coincidence between the space f h p 2 0 n n p r n and the predual space h p r n of the morrey space l p r n moreover characterizations of b h p q s r n and f h p q s r n via local means and peetre maximal functions as well as the boundedness of riesz potential operators and some singular integrals on b h p q s r n and f h p q s r n are also obtained

q spaces and morrey spaces abstract we characterize functions in morrey space by p carleson measures we then reveal a simple relation between q space and morrey space that is q space can be viewed as a fractional integration of the morrey space therefore many results for morrey space can be translated onto q space for example we show that q space is a dual space by identifying its predual

new orlicz hardy spaces associated with divergence form elliptic operators abstract let l be the divergence form elliptic operator with complex bounded measurable coefficients the positive concave function on 0 of strictly critical lower type p 0 1 and t t 1 1 t 1 for t 0 in this paper the authors study the orlicz hardy space h l r n and its dual space bmo l r n where l denotes the adjoint operator of l in l 2 r n several characterizations of h l r n including the molecular characterization the lusin area function characterization and the maximal function characterization are established the carleson measure characterization and the john nirenberg inequality for the space bmo l r n are also given as applications the authors show that the riesz transform l 1 2 and the littlewood paley g function g l map h l r n continuously into l the authors further show that the riesz transform l 1 2 maps h l r n into the classical orlicz hardy space h r n for p n n 1 1 and the corresponding fractional integral l for certain 0 maps h l r n continuously into h l r n where is determined by and and satisfies the same property as all these results are new even when t t p for all t 0 and p 0 1

some results on q p spaces 0lpl1 for p is an element of 0 1 let q p be a proper subspace of bmoa defined by means of a modified garcia norm we give a boundary value criterion for a function to be in q p and a necessary and sufficient condition in terms of p carleson measure for an

decompositions of besov hausdorff and triebel lizorkin hausdorff spaces and their applications abstract let p 1 q 1 s r and 0 1 1 max p q in this paper the authors establish the transform characterizations of besov hausdorff spaces b h p q s r n and triebel lizorkin hausdorff spaces f h p q s r n q 1 as applications the authors then establish their embedding properties which on b h p q s r n is also sharp smooth atomic and molecular decomposition characterizations for suitable moreover using their atomic and molecular decomposition characterizations the authors investigate the trace properties and the boundedness of pseudo differential operators with homogeneous symbols in b h p q s r n and f h p q s r n q 1 which generalize the corresponding classical results on homogeneous besov and triebel lizorkin spaces when p 1 and q 1 by taking 0

fefferman stein decomposition for q spaces and micro local quantities abstract in this paper we study the fefferman stein decomposition of q r n and give an affirmative answer to an open problem posed by essen et al 2000 one of our main methods is to characterize the structure of the predual of q r n by the micro local quantities this result indicates that the norm of the predual space of q r n depends on the micro local structure in a self correlation way

a new class of function spaces connecting triebel lizorkin spaces and q spaces abstract let s r 0 p 1 and q 1 in this paper we introduce a new class of function spaces f p q s r n which unify and generalize the triebel lizorkin spaces with both p 1 and p and q spaces by establishing the carleson measure characterization of q space we then determine the relationship between triebel lizorkin spaces and q spaces which answers a question posed by dafni and xiao in g dafni j xiao some new tent spaces and duality theorem for fractional carleson measures and q r n j funct anal 208 2004 377 422 moreover via the hausdorff capacity we introduce a new class of tent spaces f t p q s r n 1 and determine their dual spaces f w p q s q r n where s r p q 1 max p q 1 0 q max p q and t denotes the conjugate index of t 1 as an application of this we further introduce certain hardy hausdorff spaces f h p q s r n and prove that the dual space of f h p q s r n is just f p q s q r n when p q 1

optimal l p l q estimates for parabolic boundary value problems with inhomogeneous data in this paper we investigate vector valued parabolic initial boundary value problems mathcal a t x d mathcal b j t x d subject to general boundary conditions in domains g in mathbb r n with compact c 2m boundary the top order coefficients of mathcal a are assumed to be continuous we characterize optimal l p l q regularity for the solution of such problems in terms of the data we also prove that the normal ellipticity condition on mathcal a and the lopatinskii shapiro condition on mathcal a mathcal b 1 dots mathcal b m are necessary for these l p l q estimates as a byproduct of the techniques being introduced we obtain new trace and extension results for sobolev spaces of mixed order and a characterization of triebel lizorkin spaces by boundary data

models for variable stress accelerated life testing experiments based on wiener processes and the inverse gaussian distribution variable stress accelerated life testing trials are experiments in which each of the units in a random sample of units of a product is run under increasingly severe conditions to get information quickly on its life distribution we consider a fatigue failure model in which accumulated decay is governed by a continuous gaussian process w y whose distribution changes at certain stress change points to t l t k continuously increasing stress is also considered failure occurs the first time w y crosses a critical boundary the distribution of time to failure for the models can be represented in terms of time transformed inverse gaussian distribution functions and the parameters in models for experiments with censored data can be estimated using maximum likelihood methods a common approach to the modeling of failure times for experimental units subject to increased stress at certain stress change points is to assume that the failure times follow a distribution that consists of segments of weib

the solution of the kato square root problem for second order elliptic operators on rn we prove the kato conjecture for elliptic operators on jfin more precisely we establish that the domain of the square root of a uniformly complex elliptic operator l div av with bounded measurable coefficients in ietn is the

l2 solvability of boundary value problems for divergence form parabolic equations with complex coefficients abstract we consider parabolic operators of the form t l l div a x t in r n 2 x t x x n 1 t r n r r x n 1 0 n 1 we assume that a is a n 1 n 1 dimensional matrix which is bounded measurable uniformly elliptic and complex and we assume in addition that the entries of a are independent of the spatial coordinate x n 1 as well as of the time coordinate t for such operators we prove that the boundedness and invertibility of the corresponding layer potential operators are stable on l 2 r n 1 c l 2 r n 2 c under complex l perturbations of the coefficient matrix subsequently using this general result we establish solvability of the dirichlet neumann and regularity problems for t l by way of layer potentials and with data in l 2 assuming that the coefficient matrix is a small complex perturbation of either a constant matrix or of a real and symmetric matrix

a time discrete and zero adjusted gamma process model with application to degradation analysis abstract the standard gamma process is widely used for degradation modelling when the degradation paths are always positive and strictly increasing nevertheless the standard gamma process is considered inappropriate if the observed sample paths are horizontal over several time intervals motivated by this phenomenon we develop a time discrete and zero adjusted gamma process model statistical inference method of this model is then proposed to illustrate our proposed model both simulation study and real data analysis are conducted whose results demonstrate that the proposed model has satisfactory fit performance and predictive performance

condition based maintenance using the inverse gaussian degradation model abstract condition based maintenance has been proven effective in reducing unexpected failures with minimum operational costs this study considers an optimal condition based replacement policy with optimal inspection interval when the degradation conforms to an inverse gaussian process with random effects the random effects parameter is used to account for heterogeneities commonly observed among a product population its distribution is updated when more degradation observations are available the observed degradation level together with the unit s age are used for the replacement decision the structure of the optimal replacement policy is investigated in depth we prove that the monotone control limit policy is optimal we also provide numerical studies to validate our results and conduct sensitivity analysis of the model parameters on the optimal policy

new besov type spaces and triebel lizorkin type spaces including q spaces let s tau in mathbb r and q in 0 infty we introduce besov type spaces dot b s tau p q mathbb r n for p in 0 infty and triebel lizorkin type spaces dot f s tau p q mathbb r n rm for p in 0 infty which unify and generalize the besov spaces triebel lizorkin spaces and q spaces we then establish the varphi transform characterization of these new spaces in the sense of frazier and jawerth using the varphi transform characterization of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n we obtain their embedding and lifting properties moreover for appropriate we also establish the smooth atomic and molecular decomposition characterizations of dot b s tau p q mathbb r n rm and dot f s tau p q mathbb r n for s in mathbb r p in 1 infty q in 1 infty and tau in 0 frac 1 max p q via the hausdorff capacity we introduce certain hardy hausdorff spaces b dot h s tau p q mathbb r n and prove that the dual space of b dot h s tau p q mathbb r n is just dot b s tau p q mathbb r n where t denotes the conjugate index of t in 1 infty

homogeneous endpoint besov space embeddings by hausdorff capacity and heat equation two embeddings of a homogeneous endpoint besov space are established via the hausdorff capacity and the heat equation meanwhile a co capacity formula and a trace inequality are derived from the besov space

square roots of elliptic second order divergence operators on strongly lipschitz domains l p theory we study l p estimates for square roots of second order elliptic non necessarily selfadjoint operators in divergence form l mathrm div a nabla on lipschitz domains subject to dirichlet or to neumann boundary conditions pursuing our work 4 where we considered operators on mathbb r n we obtain among other things l 1 2 f p le c nabla f p for all 1 p infty if l is real symmetric and the domain bounded which is new for 1 p 2 we also obtain similar results for perturbations of constant coefficients operators our methods rely on a singular integral representation calderon zygmund theory and quadratic estimates a feature of this study is the use of a commutator between the resolvent of the laplacian dirichlet and neumann and partial derivatives which carries the geometry of the boundary

necessary and sufficient conditions for absolute continuity of elliptic harmonic measure our purpose in this paper is to give a necessary and sufficient condition on the modulus of continuity of the coefficients of an elliptic operator in divergence form in order that the corresponding poisson kernel for the dirichlet problem exist this condition on the coefficients is global continuity together with the additional property that the modulus of continuity along some nontangential direction at each boundary point be bounded uniformly in these points and directions by a function 7 t satisfying the dini type condition

the inverse gaussian process as a degradation model this article systematically investigates the inverse gaussian ig process as an effective degradation model the ig process is shown to be a limiting compound poisson process which gives it a meaningful physical interpretation for modeling degradation of products deteriorating in random environments treated as the first passage process of a wiener process the ig process is flexible in incorporating random effects and explanatory variables that account for heterogeneities commonly observed in degradation problems this flexibility makes the class of ig process models much more attractive compared with the gamma process which has been thoroughly investigated in the literature of degradation modeling the article also discusses statistical inference for three random effects models and model selection it concludes with a real world example to demonstrate the applicability of the ig process in degradation analysis supplementary materials for this article are available online

semiparametric estimation of gamma processes for deteriorating products this article investigates the semiparametric inference of the simple gamma process model and a random effects variant maximum likelihood estimates of the parameters are obtained through the em algorithm the bootstrap is used to construct confidence intervals a simulation study reveals that an estimation based on the full likelihood method is more efficient than the pseudo likelihood method in addition a score test is developed to examine the existence of random effects under the semiparametric scenario a comparison study using a fatigue crack growth dataset shows that performance of a semiparametric estimation is comparable to the parametric counterpart this article has supplementary material online

more risk sensitive markov decision processes we investigate the problem of minimizing a certainty equivalent of the total or discounted cost over a finite and an infinite horizon that is generated by a markov decision process mdp in contrast to a risk neutral decision maker this optimization criterion takes the variability of the cost into account it contains as a special case the classical risk sensitive optimization criterion with an exponential utility we show that this optimization problem can be solved by an ordinary mdp with extended state space and give conditions under which an optimal policy exists in the case of an infinite time horizon we show that the minimal discounted cost can be obtained by value iteration and can be characterized as the unique solution of a fixed point equation using a sandwich argument interestingly it turns out that in the case of a power utility the problem simplifies and is of similar complexity than the exponential utility case however has not been treated in the literature so far we also establish the validity and convergence of the policy improvement method a simple numerical example namely the classical repeated casino game is considered to illustrate the influence of the certainty equivalent and its parameters finally the average cost problem is also investigated surprisingly it turns out that under suitable recurrence conditions on the mdp for convex power utility the minimal average cost does not depend on the parameter of the utility function and is equal to the risk neutral average cost this is in contrast to the classical risk sensitive criterion with exponential utility

well posedness and regularity of generalized navier stokes equations in some critical q spaces we study the well posedness and regularity of the generalized navier stokes equations with initial data in a new critical space q 1 rn q rn n 12 1 which is larger than some known critical homogeneous besov spaces here q rn is a space defined as the set of all measurable functions with sup l i 2 1 n i i f x f y 2 x y n 2 1 dxdy where the supremum is taken over all cubes i with edge length l i and edges parallel to the coordinate axes in rn in order to study the well posedness and regularity we give a carleson measure characterization of q rn by investigating a new type of tent spaces and an atomic decomposition of the predual for q rn in addition our regularity results apply to the incompressible navier stokes equations with initial data in q 1 1 rn

hardy and bmo spaces associated to divergence form elliptic operators consider a second order divergence form elliptic operator l with complex bounded measurable coefficients in general operators based on l such as the riesz transform or square function may lie beyond the scope of the calderon zygmund theory they need not be bounded in the classical hardy bmo and even some l p spaces in this work we develop a theory of hardy and bmo spaces associated to l which includes in particular a molecular decomposition maximal and square function characterizations duality of hardy and bmo spaces and a john nirenberg inequality

the multi armed bandit problem decomposition and computation this paper is dedicated to our friend and mentor cyrus derman on the occasion of his 60th birthday the multi armed bandit problem arises in sequentially allocating effort to one of n projects and sequentially assigning patients to one of n treatments in clinical trials gittins and jones gittins j c jones d m 1974 a dynamic allocation index for the sequential design of experiments j gani k sarkadi l vince eds progress in statistics european meeting of statisticians 1972 1 north holland amsterdam 241 266 have shown that one optimal policy for the n project problem an n dimensional discounted markov decision chain is determined by the following largest index rule there is an index for each state of each given project that depends only on the data of that project in each period one allocates effort to a project with largest current index the purpose of this paper is to give a short proof of this result and a new characterization of the index of a project in state i viz as the maximum expected present value in state i for the restart in i problem in which in each state and period one either continues allocating effort to the project or immediately restarts the project in state i moreover it is shown that an approximate largest index rule yields an approximately optimal policy these results lead to more efficient methods of computing the indices on line and or for sparse transition matrices in large state spaces than have been suggested heretofore by using a suitable implementation of successive approximations a policy whose expected present value is within 100e of the maximum possible range of values of the indices can be found on line with at most n t 1tm operations where m is the number of operations required to calculate one approximation t is the least integer majorizing the ratio ln e ln a and 0 a 1 is the discount factor

a turnpike theorem for a risk sensitive markov decision process with stopping this paper concerns a markov decision problem with an infinite planning horizon stationary data an exponential utility function and no discounting but also with the possibility of voluntary or involuntary termination stopping this paper establishes conditions under which the expected utility of the income received by repeated use of a well chosen stationary control equals the limit as n becomes large of the optimal expected utility for the n period problem tests for these turnpike conditions are provided as is a linear program whose optimal solution determines such a control

characterizations of besov type and triebel lizorkin type spaces via maximal functions and local means abstract let s r in this paper the authors first establish the maximal function characterizations of the besov type space b p q s r n with p q 0 and 0 the triebel lizorkin type space f p q s r n with p 0 q 0 and 0 the besov hausdorff space b h p q s r n with p 1 q 1 and 0 1 max p q and the triebel lizorkin hausdorff space f h p q s r n with p q 1 and 0 1 max p q where t denotes the conjugate index of t 1 using this characterization the authors further obtain the local mean characterizations of these function spaces via functions satisfying the tauberian condition and establish a fourier multiplier theorem on these spaces all these results generalize the existing classical results on besov and triebel lizorkin spaces by taking 0 and are also new even for q spaces and hardy hausdorff spaces

generalized poincare embeddings and weighted hardy operator on qpα q spaces abstract the poincare embeddings w 1 n r n bmo r n and the john nirenberg inequality in bmo r n are classical results in modern analysis and partial differential equations this paper studies the generalized poincare embeddings and the john nirenberg inequality in q p q r n spaces furthermore for the weighted hardy operator u and its adjoint v this paper gives sufficient and necessary conditions on weight function to ensure the boundedness of them on q p q r n spaces

uniform rectifiability carleson measure estimates and approximation of harmonic functions the first author was supported by nsf grant dms 1361701 the second author was supported in part by mineco grant mtm2010 16518 icmat severo ochoa project sev 2011 0087 he also acknowledges that the research leading to these results has received funding from the european research council under the european union s seventh framework programme fp7 2007 2013 erc agreement no 615112 hapdegmt the third author was supported by the alfred p sloan fellowship the nsf career award dms 1056004 the nsf inspire award dms 1344235 and the nsf materials research science and engineering center seed grant dmr 0212302

littlewood paley characterizations of triebel lizorkin morrey spaces via ball averages abstract let 1 p u and q 1 in this article the authors establish equivalent characterizations of the triebel lizorkin morrey space e u q p r n with smoothness order 0 2 in terms of the lusin area function and the g function generated by the difference between f x and its ball average b 2 j f x 1 b x 2 j b x 2 j f y d y j 1 2 x r n where for any j 1 2 and x r n b x 2 j y r n y x 2 j as applications the authors obtain several characterizations of e u p r n via pointwise inequalities involving ball averages

some new tent spaces and duality theorems for fractional carleson measures and qα rn several duality questions for fractional carleson measures and the spaces q rn are resolved using a new type of tent spaces these tent spaces are defined in terms of choquet integrals with respect to hausdorff capacity a predual for q rn is then defined as a space of distributions containing the hardy space h1 and an atomic decomposition is proved

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

a note on m n katehakis and y r chen s computation of the gittins index in a recent paper katehakis and chen propose a sequence of linear programs for the computation of the gittins indices if there are n projects and project v has kv states then v 1nkv linear programs have to be solved in this note it is shown that instead of the kv linear programs for project v also one parametric linear program with the same dimensions can be solved

besov type spaces with variable smoothness and integrability abstract in this article the authors introduce besov type spaces with variable smoothness and integrability the authors then establish their characterizations respectively in terms of transforms in the sense of frazier and jawerth smooth atoms or peetre maximal functions as well as a sobolev type embedding as an application of their atomic characterization the authors obtain a trace theorem of these variable besov type spaces

generalized navier stokes equations with initial data in local q type spaces abstract in this paper we establish a link between leray mollified solutions of the three dimensional generalized navier stokes equations and mild solutions for initial data in the adherence of the test functions for the norm of q loc 1 r 3 this result applies to the usual incompressible navier stokes equations

splitting randomized stationary policies in total reward markov decision processes this paper studies a discrete time total reward markov decision process mdp with a given initial state distribution a randomized stationary policy can be split on a given set of states if the occupancy measure of this policy can be expressed as a convex combination of the occupancy measures of stationary policies each selecting deterministic actions on the given set and coinciding with the original stationary policy outside of this set for a stationary policy necessary and sufficient conditions are provided for splitting it at a single state as well as sufficient conditions for splitting it on the whole state space these results are applied to constrained mdps the results are refined for absorbing including discounted mdps with finite state and actions spaces in particular this paper provides an efficient algorithm that presents the occupancy measure of a given policy as a convex combination of the occupancy measures of finitely many stationary deterministic policies this algorithm generates the splitting policies in a way that each pair of consecutive policies differs at exactly one state the results are applied to constrained problems to efficiently compute an optimal policy by computing and splitting a stationary optimal policy