on the structure of the cone of positive operators abstract if k 1 is a proper cone in r n 1 and k 2 is a proper cone in r n 2 then as is well known the set k 1 k 2 which consists of all n 2 x n 1 real matrices which take k 1 into k 2 forms a proper cone in the space r n 2 n 1 in this paper a study of this cone is made with particular emphasis on its faces and duality operator a face of k 1 k 2 is called simple if it is composed of all matrices in k 1 k 2 which take some fixed face of k 1 into some fixed face of k 2 maximal faces of k 1 k 2 are characterized as a particular kind of simple faces relations between the duality operator of k 1 k 2 and those of k 1 and k 2 are obtained among many other results it is proved that d k 1 k 2 the duality operator of k 1 k 2 is injective if and only if d k 2 is injective and each face of k 1 k 2 is an intersection of simple faces two open questions are posed

the stochastic maximum principle in singular optimal control with recursive utilities abstract in this paper we consider stochastic recursive optimal control problem in which the control variable has two components with the first absolutely continuous and the second singular the control domain of the first component needs not to be convex by using a spike variation on the absolutely continuous part of the control and a convex perturbation on the singular one respectively we obtain a stochastic maximum principle of the optimal control also we give the relationship of the backward variational equation the adjoint equation and forward variational equation

computing nonnegative rank factorizations abstract the existence of nonnegative generalized inverses in terms of nonnegative rank factorizations is considered an algorithm is presented which computes a nonnegative rank factorization of a nonnegative matrix when a nonnegative 1 inverse exists

pointwise second order necessary conditions for stochastic optimal controls part i the case of convex control constraint this paper is the first part of our series of work to establish pointwise second order necessary conditions for stochastic optimal controls in this part both drift and diffusion terms may contain the control variable but the control region is assumed to be convex under some assumptions in terms of the malliavin calculus we establish the desired necessary conditions for stochastic singular optimal controls in the classical sense

locating factors of a characteristic word via the generalized zeckendorf representation of numbers let a be an irrational number with 0 1 for a factor w of f a the location of w is the set of all positions in f a at which w occurs the locations of all factors of f a have been determined by chuan and ho recently in this paper we obtain other formulas for the locations of factors of f a using the generalized zeckendorf representation of nonnegative integers these results are equivalent to the known results obtained by chuan and ho in the case a 3 52 we compute the longest common prefix of any two suffixes of f a and compute the order number and location index of each factor of f a given its length and a position in f a at which it begins

first and second order necessary conditions for stochastic optimal controls abstract the main purpose of this paper is to establish the first and second order necessary optimality conditions for stochastic optimal controls using the classical variational analysis approach the control system is governed by a stochastic differential equation in which both drift and diffusion terms may contain the control variable and the set of controls is allowed to be nonconvex only one adjoint equation is introduced to derive the first order necessary condition while only two adjoint equations are needed to state the second order necessary conditions for stochastic optimal controls

on the semiring of cone preserving maps abstract if k is a proper cone in r n then the cone of all linear operators that preserve k denoted by k forms a semiring under usual operator addition and multiplication recently j g horne examined the ideals of this semiring he proved that if k 1 k 2 are polyhedral cones such that k 1 and k 2 are isomorphic as semirings then k 1 and k 2 are linearly isomorphic the study of this semiring is continued in this paper in sec 3 ideals of k which are also faces are characterized in sec 4 it is shown that k has a unique minimal two sided ideal namely the dual cone of k where k is the dual cone of k extending horne s result it is also proved that the cone k is characterized by this unique minimal two sided ideal of k the set of all faces of k inherits a quotient semiring structure from k properties of this face semiring are given in sec 5 in particular it is proved that this face semiring admits no nontrivial congruence relation iff the duality operator of k is injective in sec 6 the maximal one sided and two sided ideals of k are identified in sec 8 it is shown that k never satisfies the ascending chain condition on principal one sided ideals some partial results on the question of topological closedness of principal one sided ideals of k are also given

brief paper stochastic maximum principle in the mean field controls in buckdahn djehiche li and peng 2009 the authors obtained mean field backward stochastic differential equations bsdes in a natural way as a limit of some highly dimensional system of forward and backward sdes corresponding to a great number of particles or agents the objective of the present paper is to deepen the investigation of such mean field bsdes by studying their stochastic maximum principle this paper studies the stochastic maximum principle smp for mean field controls which is different from the classical ones this paper deduces an smp in integral form and it also gets under additional assumptions necessary conditions as well as sufficient conditions for the optimality of a control as an application this paper studies a linear quadratic stochastic control problem of mean field type

group inverses of certain positive operators abstract positive operators on certain polyhedral cones with the property that the group inverse of the operator is equal to some power of the operator are characterized the special case of the moore penrose inverse is also considered

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

factors of characteristic words location and decompositions let a be an irrational number with 0 a 1 and let f a be the characteristic word of a the location of a factor w of f a is defined to be the set of all positions in f a at which w occurs in this paper an explicit formula of the location of each factor w of f a is obtained the decompositions red a w and sod a w of f a associated with w are established the former one involves all return words of w while the latter one involves all occurrences of w and the corresponding separate factors and overlap factors these results generalize the work by the present authors 2005 z x wen and z y wen 1994 g melancon 1999 w t cao and z y wen 2003 i m araujo and v bruyere 2005 and a glen 2006

a geometric treatment of generalized inverses and semigroups of nonnegative matrices abstract the purpose of this paper is to provide a unified treatment from the geometric viewpoint of the following closely related aspects of nonnegative matrices nonnegative matrices with nonnegative generalized inverses of various kinds nonnegative rank factorization regular elements green s relations and maximal subgroups of the semigroups of nonnegative matrices stochastic matrices column stochastic matrices and doubly stochastic matrices

maximum principle for mean field jump diffusion stochastic delay differential equations and its application to finance abstract this paper investigates a stochastic optimal control problem with delay and of mean field type where the controlled state process is governed by a mean field jump diffusion stochastic delay differential equation two sufficient maximum principles and one necessary maximum principle are established for the underlying system as an application a bicriteria mean variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques under certain conditions explicit expressions are provided for the efficient portfolio and the efficient frontier which are as elegant as those in the classical mean variance problem without delays

stochastic maximum principle for delayed doubly stochastic control systems and their applications in this paper we investigate the optimal control problems for delayed doubly stochastic control systems we first discuss the existence and uniqueness of the delayed doubly stochastic differential

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

the maximum principles for stochastic recursive optimal control problems under partial information a maximum principle for partially observed stochastic recursive optimal control problems is obtained under the assumption that control domains are not necessarily convex and forward diffusion coefficients do not contain control variables such kind of recursive optimal control problems have wide applications in finance and economics such as recursive utility optimization and principal agent problems by virtue of a classical spike variational approach and a filtering technique the maximum principle is obtained and the related adjoint processes are characterized by the solutions of forward backward stochastic differential equations in finite dimensional spaces then our theoretical results are applied to study a partially observed linear quadratic recursive optimal control problem in addition for the case with initial and terminal state constraints the corresponding maximum principle is also obtained by using ekeland s variational principle

standard sturmiam morphisms abstract we give a characterization of morphisms which preserve finite and infinite standard sturmian words the class of such morphisms coincides with the monoid d e of the endomorphisms of a where a a b generated by the two elementary morphisms e which interchanges the letter a with b and d which is the fibonacci morphism defined as d a ab d b a some new properties of these morphisms are shown in particular we prove the following result let x n n 0 be the sequence of sets inductively defined as x 0 e x 1 a x n 1 ax n for n 1 where e denotes the empty word and is the operator of left palindrome closure associating to each word w the shortest word having w as suffix for all n 0 one has x n 1 e g d x n a where denotes the identity map from this we derive a new characterization of the set per of all words w having two periods p and q which are coprimes and such that w p q 2 indeed one has that per aa xcup n 0 e l od x n a

baer semirings and baer semirings of cone preserving maps abstract the study of k the semiring of matrices which leave invariant the proper cone k is continued in this paper the definitions of baer rings and baer rings are extended to semirings at least in the case of k results that relate the concepts of right left annihilators right left facial ideals and p exposed or o p exposed faces are given proper cones k for which k is a right left baer semiring or a baer semiring are characterized in particular it is shown that k is a baer semiring if and only if k is a perfect cone the set of projections in k is investigated and its lattice structure is analyzed the concepts of equivalence of idempotents and equivalence of projections in k are introduced and examined

hamilton s principle in stochastic mechanics in this paper we establish three variational principles that provide new foundations for nelson s stochastic mechanics in the case of nonrelativistic particles without spin the resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature we first develop two stochastic variational principles whose hamilton jacobi like equations are precisely the two coupled partial differential equations that are obtained from the schrodinger equation madelung equations the two problems are zero sum noncooperative stochastic differential games that are familiar in the control theory literature they are solved here by means of a new absolutely elementary method based on lagrange functionals for both games the saddle point equilibrium solution is given by the nelson s process and the optimal controls for the two competing players are precisely nelson s current velocity v and osmotic velocity u respectively the first variational principle includes as special cases both the guerra morato variational principle phys rev d 27 1774 1983 and schrodinger original variational derivation of the time independent equation it also reduces to the classical least action principle when the intensity of the underlying noise tends to zero it appears as a saddle point action principle in the second variational principle the action is simply the difference between the initial and final configurational entropy it is therefore a saddle point entropy production principle from the variational principles it follows in particular that both v x t and u x t are gradients of appropriate principal functions in the variational principles the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second combining the two variational principles we get the quantum hamilton principle i e a variational characterization of the logarithm of the wave function the lagrangian is the lagrangian of classical mechanics with the complex valued velocity v iu replacing the classical velocity the dynamics is given by a stochastic differential equation for real valued diffusions with complex valued drift and driving noise processes from the variational principle we derive a newton type law we finally define the momentum process and show that its mean and variance coincide with those of the quantum momentum operator

infinite words with linear subword complexity abstract in section 1 we study the relations among some combinatorial properties of infinite words especially in the case of infinite words with linear subword complexity the main result of section 1 concerns a permutation property of infinite words with linear complexity in section 2 we investigate the special case of the sturmian infinite words the main result is that a sturmian infinite word associated to a real number contains no k th powers iff has a continued fraction expansion with bounded partial quotients in section 3 it is shown that some of the results of sections 1 and 2 are optimal

a study of projectionally exposed cones abstract in view of possible applications to abstract convex programs barker laidacker and poole have made an initial study of p exposed cones and o p exposed cones by restricting their attention to closed pointed cones a study of these cones is continued in this paper sufficient conditions for a face of a proper cone to be a p exposed or an o p exposed face are established characterizations of o p exposed cones among polyhedral cones are also obtained the relation between exposedness and p exposedness of faces of a general cone is examined as one consequence a question posed by iochum is answered in the finite dimensional case that is there is no finite dimensional semiregular self dual cones which are not regular also a conjecture posed by barker and thompson on p exposed faces of p n that the cone of all real polynomials of degree n which are nonnegative on the closed interval 0 1 is settled

some combinatorial properties of sturmian words abstract in this paper we give a characterization of finite sturmian words by palindrome words which generalizes a property of the fibonacci words we prove that the set st of finite sturmian words coincides with the set of the factors of all the words w such that w ab cxy with a b c palindromes x y a b and x y moreover using this result we prove that st is equal to the set of the factors of all words w having two periods p and q which are coprimes and such that w p q 2 several other combinatorial properties concerning special and bispecial elements of st are shown as a consequence we give a new and purely combinatorial proof of the enumeration formula of st

the nonnegative rank factorizations of nonnegative matrices abstract let a p m n r the set of all m n nonnegative matrices having the same rank r for matrices a in p m n n we introduce the concepts of a has only trivial nonnegative rank factorizations and a can have nontrivial nonnegative rank factorizations correspondingly the set p m n n is divided into two disjoint subsets p 1 and p 2 such that p 1 p 2 p m n n it happens that the concept of a has only trivial nonnegative rank factorizations is a generalization of a is prime in p n n n we characterize the sets p 1 and p 2 some of our results generalize some theorems in the paper of daniel j richman and hans schneider 9

well posedness of backward stochastic differential equations with general filtration abstract this paper is addressed to the well posedness of some linear and semilinear backward stochastic differential equations with general filtration without using the martingale representation theorem the point of our approach is to introduce a new notion of solution i e the transposition solution which coincides with the usual strong solution when the filtration is natural but it is more flexible for the case of general filtration than the existing notion of solutions a comparison theorem for transposition solutions and a pontryagin type stochastic maximum principle are also presented

second order taylor expansion for backward doubly stochastic control system we consider the second order taylor expansion for backward doubly stochastic control system the results are obtained under no restriction on the convexity of control domain moreover the control variable is allowed in the drift coefficient and the diffusion coefficient

martingale approach to stochastic differential games of control and stopping we develop a martingale approach for studying continuous time stochastic differential games of control and stopping in a non markovian framework and with the control affecting only the drift term of the state process under appropriate conditions we show that the game has a value and construct a saddle pair of optimal control and stopping strategies crucial in this construction is a characterization of saddle pairs in terms of pathwise and martingale properties of suitable quantities

powers in a class of a strict standard episturmian words this paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic sturmian words in particular we explicitly determine all integer powers occurring in such infinite words extending recent results of damanik and lenz d damanik d lenz powers in sturmian sequences european j combin 24 2003 377 390 doi 10 1016 s0195 6698 03 00026 x who studied powers in sturmian words the key tools in our analysis are canonical decompositions and a generalization of singular words which were originally defined for the ubiquitous fibonacci word our main results are demonstrated via some examples including the k bonacci word a generalization of the fibonacci word to a k letter alphabet k 2

applicable stochastic control from theory to practice stochastic control has come of age it is currently applied in a wide variety of fields spanning cancer research and chemotherapy economics and finance engineering management and many other areas of scientific and social investigation both theoretical models formulated to elucidate some characteristics of a problem under study and practical applications which have sought to provide specific answers to well stated problems have been the subjects of intense research for example economists have simultaneously groped with the underlying theoretical constructs justifying the adoption of particular econometric models while at the same time attempting to devise algorithms and optimization approaches to provide economic policy guidelines based on these models in the same spirit t remendous interest in options management which are based on stochastic dynamic models has stimulated much research and numerical analyses not only in universities but also in the back rooms of trading firms the usefulness of stochastic control was recognized once it became clear that it can be used as a unifying framework for treating multi stage or multi period optimization problems subject to stochastic disturbances however just as it is convenient as a formalism to formulate such problems it is becoming increasingly clear that it is practically difficult to solve them there are in fact only few problems one can solve completely and obtain optimal solutions for this reason there is today an increased awareness that a broad range of techniques including stochastic approximations perturbation techniques markov decision processes etc are an essential part of stochastic control kits it is in such a spirit that computer software such as pandore of inria the adaptive control algorithms for econometric models developed by kendrick and many others has been devised providing thereby computer aided expertise for managing stochastic control problems this software is essential even after the great effort applied to solving such problems over the last three decades ever since bellman s principle of optimality there are very few non trivial problems we can solve theoretically these include the well known linear quadratic stochastic control scp problem some version of the multi armed bandit problem and some specific linear optimization problems for example even the adaptive control problems studied over the last few years by kendrick and his co workers and presumed to be convex are believed today to include some unspecified nonconvexities private communication by d kendrick and hans amman in this spirit the intent in this paper is to introduce salient aspects of stochastic control which are useful for applications in management a review of applications can be found in neck 1984 for example as well as in books such as tapiero 1977 1988 bensoussan hurst and naslund 1974 bensoussan kleindorfer and tapiero 1978 1980 sethi and thompson 1981 kamien and schwarz 1981 malliaris and brock 1982 and whittle 1982 further due to an awesome amount of research published in this area appearing under various connotations such a task has become unwieldy rather

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

time inconsistent stochastic linear quadratic control in this paper we formulate a general time inconsistent stochastic linear quadratic lq control problem the time inconsistency arises from the presence of a quadratic term of the expected state as well as a state dependent term in the objective functional we define an equilibrium instead of optimal solution within the class of open loop controls and derive a sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we find an explicit equilibrium control as an application we then consider a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes applying the general sufficient condition we obtain explicit equilibrium strategies when the risk premium is both deterministic and stochastic

maximum principle for forward backward sdes with a general cost functional abstractin this study we consider a stochastic optimal control problem whose state variables are described by the system of forward and backward stochastic differential equations with a general cost functional which relies on the global terminal condition in the framework of frechet derivatives we derive the corresponding maximum principle via constructing a series of adjoint equations which need to be solved step by step

backward stochastic differential equations with constraints on the gains process we consider backward stochastic differential equations with convex constraints on the gains or intensity of noise process existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is lipschitz continuous in the state and gains processes and convex in the gains process it is also shown that the minimal solution can be characterized as the unique solution of a functional stochastic control type equation this representation is related to the penalization method for constructing solutions of stochastic differential equations involves change of measure techniques and employs notions and results from convex analysis such as the support function of the convex set of constraints and its various properties

lyndon words and singular factors of sturmian words abstract two different factorizations of the fibonacci infinite word were given independently in wen and wen 1994 and melancon 1996 in a certain sense these factorizations reveal a selfsimilarity property of the fibonacci word we first describe the intimate links between these two factorizations we then propose a generalization to characteristic sturmian words

general linear quadratic optimal stochastic control problems with random coefficients linear stochastic hamilton systems and backward stochastic riccati equations consider the minimization of the following quadratic cost functional j u e langle mx t x t rangle e int 0 t langle q sx s x s rangle langle n su s u s rangle ds where x is the solution of the following linear stochastic control system eq dx t a tx t b tu t dt sum i 1 d c t ix t d t iu t dw t i cr x 0 h cr u is a square integrable adapted process the problem is conventionally called the stochastic lq the abbreviation of linear quadratic problem we are concerned with the following general case the coefficients a b ci di q n and m are allowed to be adapted processes or random matrices we prove the existence and uniqueness result for the associated riccati equation which in our general case is a backward stochastic differential equation with the generator the drift term being highly nonlinear in the two unknown variables this solves bismut and peng s long standing open problem for the case of a brownian filtration which was initially proposed by the french mathematician j m bismut in seminaire de probabilites xii lecture notes in math 649 c dellacherie p a meyer and m weil eds springer verlag berlin 1978 pp 180 264 we also provide a rigorous derivation of the riccati equation from the stochastic hamilton system this completes the interrelationship between the riccati equation and the stochastic hamilton system as two different but equivalent tools for the stochastic lq problem there are two key points in our arguments the first one is to connect the existence of the solution of the riccati equation to the homomorphism of the stochastic flows derived from the optimally controlled system actually we establish their equivalence as a consequence we can construct solutions to a sequence of suitably modified riccati equations in terms of the associated stochastic hamilton systems and the optimal controls the second key point is to establish a new type of a priori estimate for solutions of riccati equations with which we show that the sequence of constructed solutions has a limit which is a solution to the original riccati equation

stochastic minimum principle for partially observed systems subject to continuous and jump diffusion processes and driven by relaxed controls in this paper we consider nonconvex control problems of stochastic differential equations driven by relaxed controls adapted in the weak star sense to a current of sigma algebras generated by observable processes we cover in a unified way both continuous diffusion and jump processes we present existence of optimal controls before we construct the necessary conditions of optimality unlike some papers in this area using only functional analysis we develop a stochastic hamiltonian system of equations on a rigorous basis using the semimartingale representation theory and the riesz representation theorem leading naturally to the existence of the adjoint process which satisfies a backward stochastic differential equation in other words our approach predicts the existence of the adjoint process as a natural consequence of riesz representation theory ensuring at the same time the weak star measurability this is unlike other papers where the adjoint process is introduced before its existence is prov

optimality conditions for stochastic boundary control problems governed by semilinear parabolic equations abstract we study the boundary control problems for stochastic parabolic equations with neumann boundary conditions imposing super parabolic conditions we establish the existence and uniqueness of the solution of state and adjoint equations with non homogeneous boundary conditions by the galerkin approximations method we also find that in this case the adjoint equation bspde has two boundary conditions one is non homogeneous the other is homogeneous by these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method

generalized inverses of cone preserving maps abstract let k 1 and k 2 be solid cones in r n and r m respectively and let a be a linear operator such that ak 1 k 2 necessary and sufficient conditions for the existence of various kinds of generalized inverses of a taking k 2 into k 1 are given projections which belong to k the set of all linear operators that preserve a are studied in particular it is proved that a projection p in k is a simplicial nonnegative linear combination of its rank one operators iff im p k is a simplical cone an open question of burns fiedler and haynsworth concerning minimal generating matrices of polyhedral cones is also extended and answered affirmatively

time inconsistent stochastic linear quadratic control characterization and uniqueness of equilibrium in this paper we continue our study on a general time inconsistent stochastic linear quadratic control problem originally formulated in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 we derive a necessary and sufficient condition for equilibrium controls via a flow of forward backward stochastic differential equations when the state is one dimensional and the coefficients in the problem are all deterministic we prove that the explicit equilibrium control constructed in y hu h jin and x y zhou siam j control optim 50 2012 pp 1548 1572 is indeed unique our proof is based on the derived equivalent condition for equilibria as well as a stochastic version of the lebesgue differentiation theorem finally we show that the equilibrium strategy is unique for a mean variance portfolio selection model in a complete financial market where the risk free rate is a deterministic function of time but all the other market parameters are possibly stochastic pro

occurrences of palindromes in characteristic sturmian words this paper is concerned with palindromes occurring in characteristic sturmian words c of slope where 0 1 is an irrational as c is a uniformly recurrent infinite word any palindromic factor of c occurs infinitely many times in c with bounded gaps our aim is to completely describe where palindromes occur in c in particular given any palindromic factor u of c we shall establish a decomposition of c with respect to the occurrences of u such a decomposition shows precisely where u occurs in c and this is directly related to the continued fraction expansion of

the relaxed optimal control problem for mean field sdes systems and application the present study deals with a new approach of optimal control problems where the state equation is a mean field stochastic differential equation and the set of strict classical controls need not be convex and the diffusion coefficient depends on the term control our consideration is based on only one adjoint process and the necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle are obtained with application to linear quadratic stochastic control problem with mean field type

generalized inverses of substochastic matrices abstract this paper looks at the question of when a substochastic matrix has a substochastic generalized inverse this question is answered for several generalized inverses including semiinverses the moore penrose inverse and the group inverse methods for constructing all such inverses are given

a maximum principle for optimal control of stochastic evolution equations a general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations the control variable and linear unbounded operators act in both drift and diffusion terms and the control set need not be convex

well posedness and regularity of backward stochastic volterra integral equations backward stochastic volterra integral equations bsvies for short are studied notion of adapted m solution is introduced well posedness of bsvies is established and some regularity results are proved for the adapted m solutions via malliavin calculus a pontryagin type maximum principle is presented for optimal controls of stochastic volterra integral equations

optimal bilinear control of stochastic nonlinear schrodinger equations mass sub critical case we study optimal control problems for stochastic nonlinear schrodinger equations in both the mass subcritical and critical case for general initial data of the minimal l 2 regularity we prove the existence and first order lagrange condition of an open loop control in particular these results apply to the stochastic nonlinear schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two respectively furthermore we obtain uniform estimates of backward stochastic solutions in new spaces of type u 2 and v 2 adapted to evolution operators related to linear schrodinger equations with lower order perturbations these estimates yield a new temporal regularity of backward stochastic solutions which is crucial for the tightness of approximating controls induced by ekeland s variational principle

a maximum principle for fully coupled stochastic control systems of mean field type abstract the present paper considers an optimal control problem for fully coupled forward backward stochastic differential equations fbsdes of mean field type in the case of controlled diffusion coefficient moreover the control domain is not assumed to be convex by virtue of a reduction method we establish the necessary optimality conditions of pontryagin s type as an application a linear quadratic stochastic control problem is studied

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

some properties of the factors of sturmian sequences in this paper we introduce the singular words of sturmian sequences which play an important role in studying the properties of the factors of sturmian sequence we also completely determine the powers of the factors the overlaps of the factors and the structure of the palindromes of the factors

palindromes and sturmian words abstract an infinite word x over the alphabet a is sturmian if and only if g x n n 1 for any integer n where g x n is the number of distinct words of length n occurring in x a palindrome is a word that can be read indistinctly from left to right or from right to left we prove that x is sturmian if and only if h x n 1 n mod 2 for any integer n where h x n is the number of palindromes of length n occurring in x an infinite word x over the alphabet a is generated by a morphism f if there exists a letter c a such that lim n f n c x we prove the existence of a morphism that generates the palindromes of any infinite sturmian word generated by a morphism

the maximum principle for partially observed optimal control of stochastic differential equations this paper concerns partially observed optimal control of possibly degenerate stochastic differential equations with correlated noises between the system and the observation the control is allowed to enter into all the coefficients a general maximum principle is proved for the partially observed optimal control and the relations among the adjoint processes are established adjoint vector fields which are adapted to the past and present observations are introduced as the solutions to some backward stochastic partial differential equations bspdes and their relations are established under suitable conditions the adjoint processes are characterized in terms of the adjoint vector fields their differentials and hessians along the optimal state process some other formulations of the partially observed stochastic maximum principle are then derived

maximum principle for singular stochastic control problems in this paper an optimal singular stochastic control problem is considered for this model a general stochastic maximum principle is obtained by using a time transformation this is the first version of the stochastic maximum principle that covers nonlinear cases

the sequence of return words of the fibonacci sequence let be a factor of the fibonacci sequence f x 1 x 2 then it occurs in the sequence infinitely many times let p be the p th occurrence of and r p be the p th return word over in this paper we study the structure of the sequence of return words r p p 1 we first introduce the singular kernel word s k for any factor of f and give a decomposition of with respect to s k using the singular kernel and the decomposition we prove that the sequence of return words over the alphabet r 1 r 2 is still a fibonacci sequence we also determine the expressions of return words completely for each factor finally we introduce the spectrum for studying some combinatorial properties such as power overlap and separate of factors