bsdes with singular terminal condition and a control problem with constraints we provide a probabilistic solution of a not necessarily markovian control problem with a state constraint by means of a backward stochastic differential equation bsde the novelty of our solution approach is that the bsde possesses a singular terminal condition we prove that a solution of the bsde exists thus partly generalizing existence results obtained by popier in stochastic process appl 116 2006 pp 2014 2056 and ann probab 35 2007 pp 1071 1117 we perform a verification and discuss special cases for which the control problem has explicit solutions

differential operators and entire functions with simple real zeros abstract let and f be functions in the laguerre polya class write z e z 2 1 z and f z e z 2 f 1 z where 1 and f 1 have genus 0 or 1 and 0 if 1 4 and has infinitely many zeros then d f z has only simple real zeros where d denotes differentiation

on weak solutions of forward backward sdes in this paper we continue exploring the notion of weak solution of forward backward stochastic differential equations fbsdes and associated forward backward martingale problems fbmps the main purpose of this work is to remove the constraints on the martingale integrands in the uniqueness proofs in our previous work ma et al in ann probab 36 6 2092 2125 2008 we consider a general class of non degenerate fbsdes in which all the coefficients are assumed to be essentially only bounded and uniformly continuous and the uniqueness is proved in the space of all the square integrable adapted solutions the standard solution space in the fbsde literature a new notion of semi strong solution is introduced to clarify the relations among different definitions of weak solution in the literature and it is in fact instrumental in our uniqueness proof as a by product we also establish some a priori estimates of the second derivatives of the solution to the decoupling quasilinear pde

the zeros of derivatives of entire functions and the polya wiman conjecture an entire function f x which assumes only real values on the real axis is said to be a real entire function thus if f is a real entire function then its maclaurin coefficients are all real and consequently the zeros of f are symmetrically located with respect to the real axis one of the intuitive principles underlying the theory of distribution of zeros of successive derivatives of real entire functions was formulated by polya p4 in his celebrated survey article entitled on the zeros of the derivatives of a function and its analytic character in this work p4 p 181 polya states the real axis seems to exert an influence on the complex zeros of f n z it seems to attract these zeros when the order is less than 2 and it seems to repel them when the order is greater than 2 indeed the first confirmation of this principle was made by alander a2 see also p6lya p2 who in 1930 showed that the polya wiman conjecture is true if the order of f x is less than 2 3 in wil and wi2 wiman established the validity of this conjecture for functions f x of order at most 1 while in 1937 polya p3 proved it for functions of order less than 4 3 a general survey of these results and related conjectures may be found in p2 and p4 for more recent surveys of this and related areas of research see boas b2 and prather pr it seems that no progress has been made on the p6lya wiman conjecture since the publication of polya s 4 3 theorem in 1937 our proof of the conjecture is self contained and does not rely on the results cited above in section 2 we will 1 introduce some definitions and notations 2 state some of the properties of functions in the laguerre p6lya class and 3 prove the polya wiman conjecture theorem 3 in the proof of theorem 3 we

backward stochastic differential equations and partial differential equations with quadratic growth we provide existence comparison and stability results for one dimensional backward stochastic differential equations bsdes when the coefficient or generator f t y z is continuous and has a quadratic growth in z and the terminal condition is bounded we also give in this framework the links between the solutions of bsdes set on a diffusion and viscosity or sobolev solutions of the corresponding semilinear partial differential equations

the lee yang and polya schur programs i linear operators preserving stability in 1952 lee and yang proposed the program of analyzing phase transitions in terms of zeros of partition functions linear operators preserving non vanishing properties are essential in this program and various contexts in complex analysis probability theory combinatorics and matrix theory we characterize all linear operators on finite or infinite dimensional spaces of multivariate polynomials preserving the property of being non vanishing whenever the variables are in prescribed open circular domains in particular this solves the higher dimensional counterpart of a long standing classification problem originating from classical works of hermite laguerre hurwitz and polya schur on univariate polynomials with such properties

hjb equations in infinite dimensions with locally lipschitz hamiltonian and unbounded terminal condition we study hamilton jacobi bellman equations in an infinite dimensional hilbert space with lipschitz coefficients where the hamiltonian has superquadratic growth with respect to the derivative of the value function and the final condition is not bounded this allows to study stochastic optimal control problems for suitable controlled state equations with unbounded control processes the results are applied to a controlled wave equation

a conservative formulation of the multidimensional upwind residual distribution schemes for general nonlinear conservation laws in the present paper we consider the numerical solution of systems of general nonlinear hyperbolic conservation laws on unstructured grids by means of the residual distribution method we propose a new formulation of the first order linear optimal positive n scheme relying on a contour integration of the convective fluxes over the boundaries of an element full conservation is achieved for arbitrary flux functions while the robustness and the monotone shock capturing of the original n scheme is retained the new variant of the n scheme is combined with the conservative second order linear lda scheme to obtain a nonlinear second order monotone b scheme the performance of the new residual distribution schemes is evaluated on problems governed by the euler equations as an application to a more complex system of conservation laws lacking an exact conservative linearization we solve the ideal magnetohydrodynamics equations in two spatial dimensions

global regular solutions of second order hamilton jacobi equations in hilbert spaces with locally lipschitz nonlinearities abstract this paper is devoted to the study of a second order hamilton jacobi equation in infinite dimensions with a locally lipschitz continuous hamiltonian h related with a stochastic optimal control problem driven by white noise in an earlier paper the author studied the case of globally lipschitz continuous hamiltonian h this paper is concerned with the case of locally lipschitz continuous h that include e g the quadratic case which appears very frequently in the applications existence uniqueness and c 2 regularity of a local solution follow by methods given previously the heart of the work is the proof of a priori estimates of the c 1 norm of the local solution this has been done by studying properties of nonlinear transition semigroups and by a careful application of them to our problem the results have been applied to a stochastic optimal control problem proving existence of feedback optimal controls

reality of the zeros of an entire function and its derivatives in 1914 p6lya raised the problem of classifying the entire functions which together with all their derivatives have only real zeros in earlier work hellerstein and williamson settled this problem for entire functions which are real on the real axis we complete the classification in all cases and show that it is sufficient to consider the function and its first two derivatives introduction in 12 and 13 g polya posed the problem of classifying all entire functions which have along with all their derivatives only real zeros he conjectured that such a function must have one of the following forms 0 1 f z aebz 0 2 f z a eicz eid 0 3 f z azme az jii l1 ez an where a and b are eomplex constants a 0 b c d and the an are real i l a2 x and m is a nonnegative integer in 10 b ja levin and i v ostrovskii showed that if f is a real i e real on the real axis entire function with only real zeros satisfying the growth condition 0 4 limsup loglog m r f rlog r x then the zeros cn of f satisfy 0 5 2 i m llcn 0oc in particular f has infinitely many nonreal zeros polya s conjecture was completely affirmed for real entire functions by two of the present authors in 6 and 7 where the cases of functions of finite order and of infinite order growth slower than that of 0 4 were successfully treated these results coupled with those of levin and ostrovskii showed that if f f and f have only real zeros and f is real entire then f is in the laguerre p6lya class i e of the form 0 3 received by the editors august 14 1981 and in revised form december 31 1981 1980 mathematics subject classification primary 30d30 secondary 30d35 partially supported by nsf grant mcs 8003108 2part of research towards ph d degree university of wisconsin 1983 american mathematical society 0002 9947 82 0000 0099 04 00

monotone residual distribution schemes for the ideal magnetohydrodynamic equations on unstructured grids multidimensional upwind residual distribution schemes are applied to the eight wave equations of ideal magnetohydrodynamics these schemes extend the high resolution upwind finite volume methodology to a truly multidimensional finite element context on unstructured grids both first and second order linear and second order nonlinear monotonicity preserving schemes are discussed an approximate conservative linearization technique is derived for general hyperbolic systems together with a conservative correction technique which guarantees the full conservation of the convective fluxes the solenoidal condition of the magnetic field is enforced by powell s source term approach both implicit and explicit time integration strategies have been implemented the spatial accuracy and the shock capturing properties of the schemes in the steady state are investigated numerically computational results are presented for a bow shock over a cylinder and for a supermagnetosonic flow in a channel

uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions in this paper we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions

mean variance hedging under partial information we consider the mean variance hedging problem under partial information the underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available we show that the initial mean variance hedging problem is equivalent to a new mean variance hedging problem with an additional correction term which is formulated in terms of observable processes we prove that the value process of the reduced problem is a square trinomial with coefficients satisfying a triangle system of backward stochastic differential equations and the filtered wealth process of the optimal hedging strategy is characterized as a solution of a linear forward equation

stochastic optimal control via forward and backward stochastic differential equations and importance sampling abstract the aim of this work is to present a novel sampling based numerical scheme designed to solve a certain class of stochastic optimal control problems utilizing forward and backward stochastic differential equations fbsdes by means of a nonlinear version of the feynman kac lemma we obtain a probabilistic representation of the solution to the nonlinear hamilton jacobi bellman equation expressed in the form of a system of decoupled fbsdes this system of fbsdes can be solved by employing linear regression techniques the proposed framework relaxes some of the restrictive conditions present in recent sampling based methods within the linearly solvable optimal control framework and furthermore addresses problems in which the time horizon is not prespecified to enhance the efficiency of the proposed scheme when treating more complex nonlinear systems we then derive an iterative algorithm based on girsanov s theorem on the change of measure which features importance sampling this scheme is shown to be capable of learning the optimal control without requiring an initial guess

sharp derivative bounds for solutions of degenerate semi linear partial differential equations abstract the paper is a continuation of the kusuoka stroock programme of establishing smoothness properties of solutions of possibly degenerate partial differential equations by using probabilistic methods we analyze here a class of semi linear parabolic partial differential equations for which the linear part is a second order differential operator of the form v 0 i 1 n v i 2 where v 0 v n are first order differential operators that satisfy the so called ufg condition see kusuoka and stroock 1987 16 which is weaker than the hormander one specifically we prove that the bounds of the higher order derivatives of the solution along the vector fields coincide with those obtained in the linear case when the boundary condition is lipschitz continuous but that the asymptotic behavior of the derivatives may change because of the simultaneity of the nonlinearity and of the degeneracy when the boundary condition is of polynomial growth and measurable only

a multidimensional exponential utility indifference pricing model with applications to counterparty risk this paper considers exponential utility indifference pricing for a multidimensional nontraded assets model subject to intertemporal default risk and provides a semigroup approximation for the utility indifference price the key tool is the splitting method whose convergence is proved based on the barles souganidis monotone scheme and the convergence rate is derived based on krylov s shaking the coefficients technique we apply our methodology to study the counterparty risk of derivatives in incomplete markets

the hurwitz type theorem for the regular coulomb wave function via hankel determinants abstract we derive a closed formula for the determinant of the hankel matrix whose entries are given by sums of negative powers of the zeros of the regular coulomb wave function this new identity applied together with results of grommer and chebotarev allows us to prove a hurwitz type theorem about the zeros of the regular coulomb wave function as a particular case we obtain a new proof of the classical hurwitz s theorem from the theory of bessel functions that is based on algebraic arguments in addition several hankel determinants with entries given by the rayleigh function and bernoulli numbers are also evaluated

extremal slabs in the cube and the laplace transform abstract we study the volume of symmetric slabs in the unit cube we show that for t 3 4 the slab parallel to a face has the minimal volume among all symmetric slabs with width t for large width we prove the asymptotic extremality of the slab orthogonal to the main diagonal the proof is based on certain concavity properties of the laplace transform and on several limit theorems from probability the central limit theorem and classical principles of moderate and large deviations finally we extend some of the results to more general classes of bodies

a fourier cosine method for an efficient computation of solutions to bsdes we develop a fourier method to solve backward stochastic differential equations bsdes a general theta discretization of the time integrands leads to an induction scheme with conditional expectations these are approximated by using fourier cosine series expansions relying on the availability of a characteristic function the method is applied to bsdes with jumps numerical experiments demonstrate the applicability of bsdes in financial and economic problems and show fast convergence of our efficient probabilistic numerical method

existence results for some quasilinear parabolic equations on considere le probleme de cauchy pour une equation dont la partie principale est un operateur parabolique quasilineaire le terme non lineaire additionnel a au plus une croissance quadratique par rapport au gradient de la solution on demontre l existence d une solution bornee faible sous des hypotheses de regularite minimales en supposant l existence d une sous solution et d une supersolution pour le probleme

a note on differential operators of infinite order a sufficient condition for entire functions f and g to be such that the series m 0 f m 0 g m m represents an entire function is established and in that case the growth of the resulting function is described

on the number of nonreal zeros of real entire functions and the fourier polya conjecture this paper is concerned with a general theorem on the number of nonreal zeros of transcendental functions j fourier formulated the theorem in his work analyse des equations determineesin 1831 but he did not give a proof roughly speaking the theorem states that if a real entire function f x can be expressed as a product of linear factors then we can count the nonreal zeros of f x by observing the behavior of the derivatives of f x on the real axis alone as we shall see in the sequel this theorem completely justifies his former argument by which he tried to prove that the function j0 2 x has only real zeros it seems that no complete proof of the theorem is known and no general theorem has been published that justifies the argument later in 1930 g polya published a paper entitled some problems connected with fourier s work on transcendental equations p3 in this paper polya conjectured two hypothetical theorems that are closely related to fourier s unproved theorem in fact he conjectured three but he proved that two of them are equivalent to each other the first hypothetical theorem is a modernized formulation of the theorem and it justifies fourier s argument completely the second conjecture was proved in 1990 but it is impossible to justify the argument using the conjecture alone in the present paper we prove polya s formulation of the theorem his first conjecture as well as its extensions give a very simple and direct proof of the second conjecture mentioned above and exhibit some applications of the results in particular we completely justify fourier s argument by our general theorems acknowledgments professor fefferman has encouraged and helped us to publish this paper the authors truly thank him for this the authors also thank professor csordas for his kind interest in the results and his valuable suggestions on the proof of the polya wiman conjecture 1 historical introduction in this section we briefly explain our results as well as their background a real entire function is an entire function that assumes only real values on the real axis fourier s unproven theorem asserts that we can know the number of nonreal zeros of such real entire functions by counting their critical points which are defined as follows let f x be a real analytic function defined in an open

quadratic bsdes with convex generators and unbounded terminal conditions in briand and hu probab theory relat fields 136 4 604 618 2006 the authors proved an existence result for bsdes with quadratic generators with respect to the variable z and with unbounded terminal conditions however no uniqueness result was stated in that work the main goal of this paper is to fill this gap in order to obtain a comparison theorem for this kind of bsdes we assume that the generator is convex with respect to the variable z under this assumption of convexity we are also able to prove a stability result in the spirit of the a priori estimates stated in karoui et al math finance 7 1 1 71 1997 with these tools in hands we can derive the nonlinear feynman kac formula in this context

the lee yang and polya schur programs ii theory of stable polynomials and applications in the first part of this series we characterized all linear operators on spaces of multivariate polynomials preserving the property of being nonvanishing in products of open circular domains for such sets this completes the multivariate generalization of the classification program initiated by polya and schur for univariate real polynomials we build on these classification theorems to develop here a theory of multivariate stable polynomials applications and examples show that this theory provides a natural framework for dealing in a uniform way with lee yang type problems in statistical mechanics combinatorics and geometric function theory in one or several variables in particular we answer a question of hinkkanen on multivariate apolarity

optimal control for stochastic volterra equations with completely monotone kernels in this paper we study a class of optimal control problems for stochastic volterra equations in infinite dimensions we are concerned with a class of stochastic volterra integro differential problem with completely monotone kernels where we assume that the noise enters the system when we introduce a control we provide a semigroup setting for the problem by the state space setting the applications to optimal control provide other interesting results and require a precise description of the properties of the generated semigroup in our stochastic optimal control problems the drift term of the equation has a linear growth in the control variable the cost functional has a quadratic growth and the control process belongs to the class of square integrable adapted processes with no bound assumed on it our main results are the existence for the optimal feedback control the identification of the optimal cost with the value y 0 of the maximal solution y z of the backward stochastic differential equation the existence of a weak solution to the so called closed loop equation and finally the construction of an optimal feedback in terms of the process z

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

notes on the eigensystem of magnetohydrodynamics the eigenstructure of the equations governing one dimensional ideal magnetohy drodynamics is examined motivated by the wish to exploit it for construction of high resolution computational algorithms the results are given in simple forms that avoid indeterminacy or degeneracy whenever possible the unavoidable indeterminacy near the magnetosonic or triple umbilic state is analysed and shown to cause no difficulty in evaluating a numerical flux function the structure of wave paths close to this singularity is obtained and simple expressions are presented for the structure coefficients that govern wave steepening

non real zeros of real differential polynomials the main results of the paper determine all real meromorphic functions f of finite lower order in the plane such that f has finitely many zeros and non real poles and certain combinations of derivatives of f have few non real zeros msc 2000 30d20 30d35

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

on a class of stochastic optimal control problems related to bsdes with quadratic growth in this paper we study a class of stochastic optimal control problems where the drift term of the equation has a linear growth on the control variable the cost functional has a quadratic growth and the control process takes values in a closed set not necessarily compact this problem is related to some backward stochastic differential equations bsdes with quadratic growth and unbounded terminal value we prove that the optimal feedback control exists and the optimal cost is given by the initial value of the solution of the related bsde

backward stochastic partial differential equations with quadratic growth abstract this paper is concerned with the weak solution in analytic sense to the cauchy dirichlet problem of a backward stochastic partial differential equation when the nonhomogeneous term has a quadratic growth in both the gradient of the first unknown and the second unknown existence and uniqueness results are obtained under separate conditions

bsde driven by poisson point processes with discontinuous coefficient abstract in this paper we deal with the one dimensional backward stochastic differential equation bsde driven by poisson processes by means of the comparison theorem we first prove the existence of a minimal solution for bsde where the coefficient is continuous and satisfies an improved linear growth assumption then we extend the result to the case where the coefficient is left or right continuous

proof of a conjecture of polya on the zeros of successive derivatives of real entire functions we prove polya s conjecture of 1943 for a real entire function of order greater than 2 with finitely many non real zeros the number of non real zeros of the nth derivative tends to infinity as n to infty we use the saddle point method and potential theory combined with the theory of analytic functions with positive imaginary part in the upper half plane

differentiation evens out zero spacings if f is a polynomial with all of its roots on the real line then the roots of the derivative f are more evenly spaced than the roots of f the same holds for a real entire function of order 1 with all its zeros on a line in particular we show that if f is entire of order 1 and has sufficient regularity in its zero spacing then under repeated differentiation the function approaches after normalization the cosine function we also study polynomials with all their zeros on a circle and we find a close analogy between the two situations this sheds light on the spacing between zeros of the riemann zeta function and its connection to random matrix polynomials

backward stochastic differential equations associated with the vorticity equations abstract in this paper we derive a non linear version of the feynman kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions we prove the existence global in time and uniqueness for a stochastic terminal value problem associated with the vorticity equation in dimension 2 a particular class of terminal values provide via these probabilistic methods solutions for the vorticity equation

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

existence of optimal stochastic controls and global solutions of forward backward stochastic differential equations we consider an optimal stochastic control problem assuming lipschitz conditions and allowing degeneracy of the diffusion coefficient under some structural constraint on the state equation we formulate the problem in the strong form i e we fix the probability space we relate the value function and the feedback law to a forward backward stochastic differential system we prove existence and uniqueness of a global solution to the latter and deduce existence and in some cases uniqueness of an optimal control to solve the coupled forward backward system we use a priori estimates which follow from its control theoretic interpretation

differential operators of infinite order and the distribution of zeros of entire functions whenever the right hand side of 1 2 represents an analytic function in a neighborhood of the origin when x is an entire function the operator d has been studied by several authors see for example 5 11 19 chapter ix 22 and 32 the conjecture of polya and wiman proved in 8 9 and 17 states that if f x l p then df x is in the laguerre polya class for all sufficiently large positive integers m in this paper we analyze the more general situation when d is replaced by the operator d in section 2 we consider real power series with zero linear term i e 1 0 in 1 1 and 0 2 0 and show that if f x is any real polynomial then d f x l p for all sufficiently large positive integers m theorem 2 4 if the linear term in 1 1 is nonzero

the fox wright functions and laguerre multiplier sequences abstract linear operators which 1 preserve the reality of zeros of polynomials having only real zeros and 2 map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain fox wright functions and generalized mittag leffler functions the paper includes several open problems and questions

universal oscillations of high derivatives differentiation generates oscillations for the n th derivative f n t of a function f t that is analytic in a strip including the real t axis the oscillations occupy a t interval that gets larger as n increases the oscillations are studied in detail using integral representations and large n asymptotics for functions with singularities poles or branch points in the complex t plane the oscillations of high derivatives are determined by the singularities for entire functions the oscillations originate in complex saddle points in a wide class of cases the oscillations are contained in a gaussian envelope in the t interval where f n t is largest with the envelope including about graphic 1 oscillations examples of the universal oscillations are given for f t with a simple pole competing branch points a single saddle competing pole and saddle and where the zeros are confined to half the real axis 1 embed inline graphic 1 gif

evolution of superoscillations for schrodinger equation in a uniform magnetic field aharonov berry superoscillations are band limited functions that oscillate faster than their fastest fourier component superoscillations appear in several fields of science and technology such as aharonov s weak measurement in quantum mechanics in optics and in signal processing an important issue is the study of the evolution of superoscillations using the schrodinger equation when the initial datum is a weak value some superoscillatory functions are not square integrable but they are real analytic functions that can be extended to entire holomorphic functions this fact leads to the study of the continuity of a class of convolution operators acting on suitable spaces of entire functions with growth conditions in this paper we study the evolution of a superoscillatory initial datum in a uniform magnetic field moreover we collect some results on convolution operators that appear in the theory of superoscillatory functions using a direct approach that allows the convolution operators to have non

quadratic bsde with mathbb l 2 terminal data krylov s estimate ito krylov s formula and existence results we establish a krylov type estimate and an ito krylov change of variable formula for the solutions of one dimensional quadratic backward stochastic differential equations qbsdes with a measurable generator and an arbitrary terminal datum this allows us to prove various existence and uniqueness results for some classes of qbsdes with a square integrable terminal condition and sometimes a merely measurable generator it turns out that neither the existence of exponential moments of the terminal datum nor the continuity of the generator are necessary to the existence and or uniqueness of solutions we also establish a comparison theorem for solutions of a particular class of qbsdes with measurable generator as a byproduct we obtain the existence of viscosity solutions for a particular class of quadratic partial differential equations qpdes with a square integrable terminal datum

bsdes with polynomial growth generators in a defaultable market abstract in this paper we study a backward stochastic differential equation bsde for short driven by a brownian motion and a jump martingale in a defaultable setting with a polynomial growth generator this kind of bsde has important applications to the defaultable market to demonstrate this in a strict way we first prove the existence uniqueness and uniform p p 2 estimate of its solution then two examples are given to illustrate its applications to recursive utility and contingent claim hedging

polya schur master theorems for circular domains and their boundaries we characterize all linear operators on finite or infinite dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region omega subset of c for arbitrary

stochastic control for a class of nonlinear kernels and applications we consider a stochastic control problem for a class of nonlinear kernels more precisely our problem of interest consists in the optimization over a set of possibly non dominated probability measures of solutions of backward stochastic differential equations bsdes since bsdes are non linear generalizations of the traditional linear expectations this problem can be understood as stochastic control of a family of nonlinear expectations or equivalently of nonlinear kernels our first main contribution is to prove a dynamic programming principle for this control problem in an abstract setting which we then use to provide a semimartingale characterization of the value function we next explore several applications of our results we first obtain a wellposedness result for second order bsdes as introduced in 76 which does not require any regularity assumption on the terminal condition and the generator then we prove a non linear optional decomposition in a robust setting extending recent results of 63 which we then use to obtain a superhedging duality in uncertain incomplete and non linear financial markets finally we relate under additional regularity assumptions the value function to a viscosity solution of an appropriate path dependent partial differential equation ppde

on the backward stochastic riccati equation in infinite dimensions we study backward stochastic riccati equations bsres arising in quadratic optimal control problems with infinite dimensional stochastic differential state equations we allow the coefficients both in the state equation and in the cost to be random in such a context bsres are backward stochastic differential equations existing in a non hilbert space and involving quadratic nonlinearities we propose two different notions of solutions to bsres and prove for both of them existence and uniqueness results we also show that such solutions allow us to perform the synthesis of the optimal control finally we apply our results to the optimal control of a delay equation and of a wave equation with random damping

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

on the de bruijn newman constant abstract if 0 denotes the infimum of the set of real numbers such that the entire function represented by t 0 e 4 log x 2 i t 2 log x x 5 4 n 1 2 n 4 2 x 3 n 2 e n 2 x d x x has only real zeros then the de bruijn newman constant is defined as 4 0 the riemann hypothesis is equivalent to the inequality 0 the fact that the non trivial zeros of the riemann zeta function lie in the strip s 0 re s 1 and a theorem of de bruijn imply that 1 2 in this paper we prove that all but a finite number of zeros of are real and simple for each 0 and consequently that 1 2

on the polya wiman properties of differential operators abstract let x n x n be a formal power series with real coefficients and let d denote differentiation it is shown that for every real polynomial f there is a positive integer m 0 such that d m f has only real zeros whenever m m 0 if and only if 0 0 or 2 0 2 1 2 0 and that if does not represent a laguerre polya function then there is a laguerre polya function f of genus 0 such that for every positive integer m d m f represents a real entire function having infinitely many nonreal zeros

indefinite stochastic riccati equations this paper is concerned with stochastic riccati equations sres which are a class of matrix valued nonlinear backward stochastic differential equations bsdes the sres under consideration are in general indefinite in the sense that certain parameter matrices are indefinite this kind of equations arises from the stochastic linear quadratic lq optimal control problem with random coefficients and indefinite state and control weighting costs the latter having profound implications in both theory and applications while the solvability of the sres is the key to solving the indefinite stochastic lq control it remains in general an extremely difficult open problem this paper attempts to solve the problem of existence and uniqueness of solutions to the indefinite sres for a number of special yet important cases

optimal control problem for stochastic evolution equations in hilbert spaces in this article we consider an optimal control problem in which the controlled state dynamics is governed by a stochastic evolution equation in hilbert spaces and the cost functional has a quadratic growth the existence and uniqueness of the optimal control are obtained by the means of an associated backward stochastic differential equations with a quadratic growth and an unbounded terminal value as an application an optimal control of stochastic partial differential equations with dynamical boundary conditions is also given to illustrate our results

on the zeros of the derivatives of real entire functions and wiman s conjecture let f be an entire function of finite order real on the real axis and possessing only real zeros a classical problem proposed by g p6lya 9 10 and a wiman 1 is to determine from the hadamard canonical representation of the function the number of nonreal zeros of the higher derivatives of f in this paper we shall prove the following conjecture of wiman which has been open since 1915