nonlinear kolmogorov equations in infinite dimensional spaces the backward stochastic differential equations approach and applications to optimal control solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations parabolic equations are intended in a mild sense that reveals to be suitable also towards applications to optimal control

properties of two dimensional maximum entropy power spectrum estimates in this paper we present the results of a number of experiments that have been performed to study the properties of two dimensional maximum entropy spectral estimates the results presented include studies on the resolution differences for real and complex data resolution properties of the spectral estimates and the determination of the relative power of the sinusoids from the spectral estimates the results also include the effects of signal to noise ratio size and shape of the known autocorrelation region and data length and initial phase of a sinusoid on the spectral estimates in most cases studied the properties of two dimensional maximum entropy spectral estimates can be viewed as simple extensions of their one dimensional counterparts

linear quadratic partially observed forward backward stochastic differential games and its application in finance abstract this paper is concerned with a partially observed linear quadratic game problem driven by forward backward stochastic differential equations where the forward diffusion coefficients do not contain control variables and the control domains are not necessarily convex the drift term of the observation equation is linear with respect to the state and there is correlated noise between the state and the observation equation by virtue of the classical spike variational method and the backward separation technique we derive a necessary and a sufficient condition of the stochastic differential game problem then we obtain filtering equations and present a feedback representation form of the equilibrium point through riccati equations as a practical application we solve a partial information investment problem involving g expectation as a convex risk measurement and give the numerical simulation to show the explicit investment strategy and illustrate some reasonable phenomena influenced by common financial parameters

stochastic optimal control with delay in the control ii verification theorem and optimal feedbacks we consider a stochastic optimal control problem governed by a stochastic differential equation with delay in the control using an existence and uniqueness result of a sufficiently regular mild solution of the associated hamilton jacobi bellman equation see the companion paper f gozzi and f masiero siam j control optim 55 2017 pp 2981 3012 we solve the control problem by proving a verification theorem and the existence of optimal feedback controls

feedbacks for nonautonomous regular linear systems we introduce nonautonomous well posed and absolutely regular linear systems as quadruples consisting of an evolution family and output input and input output maps subject to natural hypotheses in the spirit of weiss work these maps are represented in terms of admissible observation and control operators the latter in an approximate sense in the time domain in this setting the closed loop system exists for a canonical class of admissible feedbacks and it inherits the absolute regularity and other properties of the given system in particular we can iterate feedbacks

existence conditions and variational approach for adapted solutions of the two point boundary value problem of stochastic differential equations abstract this paper considers the two point boundary value problem of stochastic differential equation with the following form dx t f t x t dt t x t dw t ax 0 bx t the sufficient and necessary conditions are given for the existence of the adapted solutions in the simple case that f t xt ft the solution can be obtained by introducing a control term ft extending the solution from xt to xt ft and constructing a process sequence all the results obtained are compared with those related to the eigenvalue problems and the martingale approach solution proposed by pardoux and peng for backward stochastic differential equations

stability of a heat exchanger feedback control system using the circle criterion the standard linearized model of a controlled heat exchanger in the form of a system of two first order pdes is interpreted as an abstract semigroup system on an appropriately selected hilbert state space we analyse some its basis properties exponential stability admissibility of an observation functional and regularity of the system impulse response next we give a proof of a version of the circle criterion which bases on the use of the leray schauder fixed point theorem jointly with a uniqueness result the circle criterion is then implemented to a feedback control system of the heat exchanger with a proportional controller and a non linear valve in the feedback loop all considerations are illustrated by a numerical example of the heat exchanger installed in central heating system at the agh university of science and technology cracow poland for which we estimate feasible settlements of the proportional controller

numerical methods for a class of nonlocal diffusion problems with the use of backward sdes we propose a novel numerical approach for nonlocal diffusion equations du et al 2012 with integrable kernels based on the relationship between the backward kolmogorov equation and backward stochastic differential equations bsdes driven by levy jumps processes the nonlocal diffusion problem under consideration is converted to a bsde for which numerical schemes are developed as a stochastic approach the proposed method completely avoids the challenge of iteratively solving non sparse linear systems arising from the nature of nonlocality this allows for embarrassingly parallel implementation and also enables adaptive approximation techniques to be incorporated in a straightforward fashion moreover our method recovers the convergence rates of classic deterministic approaches e g finite element or collocation methods due to the use of high order temporal and spatial discretization schemes in addition our approach can handle a broad class of problems with general inhomogeneous forcing terms as long as they are globally lipschitz continuous rigorous error analysis of the new method is provided as several numerical examples that illustrate the effectiveness and efficiency of the proposed approach

existence uniqueness and invariant measures for stochastic semilinear equations on hilbert spaces a class of stochastic evolution equations with additive noise and weakly continuous drift is considered first regularity properties of the corresponding ornstein uhlenbeck transition semigrouprt are obtained we show thatrt is a compactc0 semigroup in all sobolev spaceswn p which are built on its invariant measure then we show the existence uniqueness compactness and smoothing properties of the transition semigroup for semilinear equations inlp spaces and spacesw1 p as a consequence we prove the uniquencess of martingale solutions to the stochastic equation and the existence of a unique invariant measure equivalent to it is shown also that the density of this measure with respect to is inlp for allp 1

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

infinite horizon backward stochastic differential equations and elliptic equations in hilbert spaces solutions of semilinear elliptic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations the backward equation is considered on an infinite time horizon and a suitable growth condition replaces the final condition elliptic equations are intended in a mild sense suitable also for applications to optimal control we finally notice that due to the lack of smoothing properties the elliptic partial differential equation considered here could not be treated by analytic methods

homogenization of random semilinear pdes we prove a homogenization result for system of semilinear parabolic pdes of the type where v and a are random ergodic fields we extend to the random case results of buckdahn hu peng 4 for periodic structures the same method involving stability results is applied our main tool is an l p estimate for the gradient of the solution of the auxiliary problems the same type of resultsis obtained for systems of semilinear elliptic pdes

stochastic optimal control problems and parabolic equations in banach spaces we consider stochastic optimal control problems in banach spaces these problems are related to nonlinear controlled equations with dissipative nonlinearity and are treated via the backward stochastic differential equation approach which also allows us to solve in a mild sense hamilton jacobi bellman equations in banach spaces we apply the results to controlled stochastic heat and wave equations with a cost functional that is well defined on continuous functions and to delay equations in spaces of p integrable functions

infinite horizon and ergodic optimal quadratic control for an affine equation with stochastic coefficients we study stochastic optimal control problems with a quadratic cost and linear state equation that involves stochastic coefficients and control dependent noise and moreover is perturbed by an affine term both the infinite horizon case and the ergodic case are treated to this purpose we introduce a backward stochastic riccati equation and a dual backward stochastic equation both considered in the whole time line besides some stabilizability conditions we prove the existence of a solution for the two previous equations defined as limit of suitable finite horizon approximating problems this allows us to perform the synthesis of the optimal control

necessary and sufficient conditions for near optimality in stochastic control of fbsdes abstract we consider control problems for systems governed by a nonlinear forward backward stochastic differential equation fbsde we establish necessary as well as sufficient conditions for near optimality satisfied by all near optimal controls these conditions are described by two adjoint processes corresponding to the forward and backward components and a nearly maximum condition on the hamiltonian the proof of the main result is based on ekeland s variational principle and some estimates on the state and the adjoint processes with respect to the control variable as is well known optimal controls may fail to exist even in simple cases this justifies the use of near optimal controls which exist under minimal assumptions and are sufficient in most practical cases moreover since there are many nearly optimal controls it is possible to choose suitable ones that are convenient for implementation

eventual regularity of the semigroup associated with the mono tubular heat exchanger equation with output feedback this paper is concerned with the regularity of the mono tubular heat exchanger equation with output feedback by approach of spectrum analysis it is shown that the semigroup generated by the closed loop operator consisting of the mono tubular heat exchanger equation and the output feedback law is eventually differentiable and eventually compact

well posedness of semilinear stochastic wave equations with holder continuous coefficients abstract we prove that semilinear stochastic abstract wave equations including wave and plate equations are well posed in the strong sense with an holder continuous drift coefficient if 2 3 1 the uniqueness may fail for the corresponding deterministic pde and well posedness is restored by adding an external random forcing of white noise type this shows a kind of regularization by noise for the semilinear wave equation to prove the result we introduce an approach based on backward stochastic differential equations we also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results

characterizing three dimensional wavefields with high resolution spectra three dimensional spectra frequency x wavenumber y wavenumber or f kx ky spectra can be used to determine the frequency content velocity and direction of waves entering an array of receivers this information is important in detecting aliasing problems understanding coherent noise designing arrays and determining parameters for coherent noise filters because of the limited spatial dimensions of most arrays the discrete fourier transform produces an estimate of the three dimensional 3 d spectrum with severe wavenumber distortion we extend a 2 d hybrid spectral estimation method to three dimensions by combining a temporal fourier transform with a spatial 2 d maximum entropy spectral estimation technique the method produces f kx ky spectra with higher wavenumber resolution and less spectral distortion than corresponding 3 d fourier spectra the 2 d maximum entropy spectral estimation algorithm uses a sequence of fourier transforms to extrapolate the estimated autocorrelation function of the data

infinite horizon stochastic optimal control for volterra equations with completely monotone kernels abstract the aim of the paper is to study an optimal control problem on infinite horizon for an infinite dimensional integro differential equation with completely monotone kernels where we assume that the noise enters the system when we introduce a control we start by reformulating the state equation into a semilinear evolution equation which can be treated by semigroup methods the application to optimal control provides other interesting results and requires a precise description of the properties of the generated semigroup the main tools consist in studying the differentiability of the forward backward system with infinite horizon corresponding with the reformulated problem and the proof of existence and uniqueness of mild solutions to the corresponding hamilton jacobi bellman hjb equation

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

quasi linear pdes and forward backward stochastic differential equations weak solutions abstract in this paper we study the existence uniqueness and the probabilistic representation of the weak solutions of quasi linear parabolic and elliptic partial differential equations pdes in the sobolev space h 1 r d for this we study first the solutions of forward backward stochastic differential equations fbsdes with smooth coefficients regularity of solutions and their connection with classical solutions of quasi linear parabolic pdes then using the approximation procedure we establish their convergence in the sobolev space to the solutions of the fbsdes in the space l 2 r d r d l 2 r d r k l 2 r d r k d this gives a connection with the weak solutions of quasi linear parabolic pdes finally we study the unique weak solutions of quasi linear elliptic pdes using the solutions of the fbsdes on infinite horizon

necessary conditions for optimal control of stochastic systems with random jumps a maximum principle is proved for optimal controls of stochastic systems with random jumps the control is allowed to enter into both diffusion and jump terms the form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system the word pure here means the absence of the jump term in calculating the first order coefficient for the cost variation only a property for lebesgue integrals of scalar valued functions in the real number space cal r is used this shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned

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

mild solutions of semilinear elliptic equations in hilbert spaces abstract this paper extends the theory of regular solutions c 1 in a suitable sense for a class of semilinear elliptic equations in hilbert spaces the notion of regularity is based on the concept of g derivative which is introduced and discussed a result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property that is it maps continuous functions into g differentiable ones the validity of this smoothing assumption is fully discussed for the case of the ornstein uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature it is shown that the results apply to hamilton jacobi bellman hjb equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that in particular they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now

adaptive boundary and point control of linear stochastic distributed parameter systems an adaptive control problem for the boundary or the point control of a linear stochastic distributed parameter system is formulated and solved in this paper the distributed parameter system is modeled by an evolution equation with an infinitesimal generator for an analytic semigroup since there is boundary or point control the linear transformation for the control in the state equation is also an unbounded operator the unknown parameters in the model appear affinely in both the infinitesimal generator of the semigroup and the linear transformation of the control strong consistency is verified for a family of least squares estimates of the unknown parameters an ito formula is established for smooth functions of the solution of this linear stochastic distributed parameter system with boundary or point control the certainty equivalence adaptive control is shown to be self tuning by using the continuity of the solution of a stationary riccati equation as a function of parameters in a uniform operator topology for a quadratic cost functional of the state and the control the certainty equivalence control is shown to be self optimizing that is the family of average costs converges to the optimal ergodic cost some examples of stochastic parabolic problems with boundary control and a structurally damped plate with random loading and point control are described that satisfy the assumptions for the adaptive control problem solved in this paper

viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions iii uniqueness of viscosity solutions for general second order equations we prove here the uniqueness and existence of viscosity solutions for a general class of fully nonlinear second order equations in an infinite dimensional hilbert space the uniqueness is proved using the so called inf and sup convolutions which allow some reduction to finite dimensional problems

homogenization of elliptic equations with principal part not in divergence form and hamiltonian with quadratic growth in this paper we consider the following problem here the coefficients aij and bi are smooth periodic with respect to the second variable and the matrix aij ij is uniformly elliptic the hamiltonian h is locally lipschitz continuous with respect to u and du and has quadratic growth with respect to du the hamilton jacobi beliman equations of some stochastic control problems are of this type our aim is to pass to the limit in 0 as tends to zero we assume the coefficients bi to be centered with respect to the invariant measure of the problem see the main assumption 3 13 then we derive l h and w p0 2 estimates for the solutions of 0 we also prove the following corrector s result this allows us to pass to the limit in 0 and to obtain this problem is of the same type as the initial one when 0 is the hamilton jacobi bellman equation of a stochastic control problem then 00 is also a hamilton jacobi bellman equation but one corresponding to a modified set of controls

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

generalized solutions of hjb equations applied to stochastic control on hilbert space abstract in this paper we prove the existence of borel measurable optimal control laws for infinite dimensional nonstationary stochastic control problems on hilbert space this is based on some recent results on existence of generalized solutions of hjb equations on hilbert space l2 h where is a suitable reference measure on h for illustration some examples are presented

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

ergodic control of multidimensional diffusions 1 the existence results the existence of optimal stable markov relaxed controls for the ergodic control of multidimensional diffusions is established by direct probabilistic methods based on a characterization of a s limit sets of empirical measures the optimality of the above is established in the strong i e almost sure sense among all admissible controls under very general conditions

stability of bsdes with random terminal time and homogenization of semilinear elliptic pdes in this paper we extend the probabilistic method for homogenization of semi linear parabolic pdes developed by buckdahn hu and peng to the case of elliptic pdes first we give a stability result for bsdes with random terminal time which are related to elliptic pdes as shown in peng stochastics stochastics rep 37 1991 61 74 in the one dimensional case we also partially relax the monotonicity assumption on the coefficient then we use these stability results for bsdes with random terminal time to study homogenization of systems of semilinear elliptic pdes

probabilistic approach to singular perturbations of semilinear and quasilinear parabolic pdes in 5 buckdahn et al study some homogenization properties of systems of semilinear parabolic partial di erential equations pdes in short with periodic structures using a probabilistic approach involving stability of backward stochastic di erential equations bsdes this method is also developed in 3 to take into account systems of semilinear elliptic pdes which are related to bsdes with random terminal time moreover buckdahn and hu in 4 deal with homogenization of quasilinear pdes showing o some kind of stability property of forward backward stochastic di erential equations fbsdes in short in this paper we adopt the same method in order to study singular perturbations of semilinear pdes as well as those of quasilinear pdes the strong stability properties of bsdes allow us to study the asymptotic behavior of the solution of a system of singularly perturbed semilinear pdes by using the nonlinear feynman kac formula developed by pardoux and peng 11 singular perturbations of quasi linear pdes are treated in the same way in view of their connections to fbsdes revealed by ma et al 13

regular solutions of second order stationary hamilton jacobi equations abstract we study a second order stationary hamilton jacobi equation in infinite dimension this equation is nonlinear and convex with respect to the first order term we use properties of the transition semigroup associated to the linear equation to write the hamilton jacobi equation in integral form and we prove existence uniqueness and regularity of a solution by the theory of maximal monotone operators we also prove that this solution is the pointwise limit of a uniformly bounded sequence of classical solutions of approximating problems finally the solution is the value function of the associated optimal stochastic control problem some examples are given

ergodic bsdes and optimal ergodic control in banach spaces in this paper we introduce a new kind of backward stochastic differential equations called ergodic bsdes which arise naturally in the study of optimal ergodic control we study the existence uniqueness and regularity of solution to ergodic bsdes then we apply these results to the optimal ergodic control of a banach valued stochastic state equation we also establish the link between the ergodic bsdes and the associated hamilton jacobi bellman equation applications are given to the optimal ergodic control of stochastic partial differential equations

stochastic equations with delay optimal control via bsdes and regular solutions of hamilton jacobi bellman equations we consider an ito stochastic differential equation with delay driven by brownian motion whose solution by an appropriate reformulation defines a markov process x with values in a space of continuous functions mathbf c with generator mathcal l we then consider a backward stochastic differential equation depending on x with unknown processes y z and we study properties of the resulting system in particular we identify the process z as a deterministic functional of x we next prove that the forward backward system provides a suitable solution to a class of parabolic partial differential equations on the space mathbf c driven by mathcal l and we apply this result to prove a characterization of the fair price and the hedging strategy for a financial market with memory effects we also include applications to optimal stochastic control of differential equation with delay in particular we characterize optimal controls as feedback laws in terms of the process x

ergodic bsdes driven by markov chains we consider ergodic backward stochastic differential equations bsdes in a setting where noise is generated by a countable state uniformly ergodic markov chain we show that for lipschitz drivers such that a comparison theorem holds these equations admit unique solutions to obtain this result we show by coupling and splitting techniques that uniform ergodicity estimates of markov chains are robust to perturbations of the rate matrix and that these perturbations correspond in a natural way to ergodic bsdes we then consider applications of this theory to markov decision problems with a risk averse average reward criterion

adaptive control for semilinear stochastic systems an adaptive ergodic cost stochastic control problem for a partially known semilinear stochastic system in an infinite dimensional space is formulated and solved the solutions of the hamilton jacobi bellman equations for the discounted cost and the ergodic cost stochastic control problems require some special interpretations because they do not typically exist in the usual sense the solutions of the parameter dependent ergodic hamilton jacobi bellman equations are obtained from some corresponding discounted cost control problems as the discount rate tends to zero the solutions of the ergodic hamilton jacobi bellman equations are shown to depend continuously on the parameter a certainty equivalence adaptive control is given that is based on the optimal controls from the solutions of the ergodic hamilton jacobi bellman equations and a strongly consistent family of estimates of the unknown parameter this adaptive control is shown to achieve the optimal ergodic cost for the known system

optimal control problems for stochastic delay evolution equations in banach spaces we consider the optimal control for a banach space valued stochastic delay evolution equation the existence and uniqueness of the mild solution for the associated hamilton jacobi bellman equations are obtained by means of backward stochastic differential equations an application to optimal control of stochastic delay partial differential equations is also given

brief infinite horizon backward stochastic differential equation and exponential convergence index assignment of stochastic control systems this paper studies exponential convergence index assignment of stochastic control systems from the viewpoint of backward stochastic differential equation like deterministic control systems it is shown that the exact controllability of an open loop stochastic system is equivalent to the possibility of assigning an arbitrary exponential convergence index to the solution of the closed loop stochastic system formed by means of suitable linear feedback of the states as an application a sufficient and necessary condition for the existence and uniqueness of the solution of a class of infinite horizon forward backward stochastic differential equations is provided

bsdes driven by g brownian motion with time varying lipschitz condition abstract the present paper is devoted to the study of backward stochastic differential equations driven by g brownian motion g bsdes with time varying lipschitz condition with the help of nonlinear stochastic analysis technique and approximation method we prove that the g bsdes admit a unique solution on finite or infinite time horizon furthermore we obtain the corresponding comparison theorem

two stream counter flow heat exchanger equation with time varying velocities abstract we study the two stream counter flow heat exchanger equation with time varying fluid velocities formulating it into a time varying boundary control system a representation formula of the solution is obtained

backwards sde with random terminal time and applications to semilinear elliptic pde suppose im t is the filtration induced by a wiener process w in r d tau is a finite im t stopping time terminal time xi is an im tau measurable random variable in r k terminal value and f cdot y z is a coefficient process depending on y in r k and z in l r d r k satisfying y tilde y f s y z f s tilde y z leq a y tilde y 2 f need not be lipschitz in y and f s y z f s y tilde z leq b z tilde z for some real a and b plus other mild conditions we identify a hilbert space depending on tau and on the number gamma equiv b 2 2a in which there exists a unique pair of adapted processes y z satisfying the stochastic differential equation dy s 1 s leq tau z s dw s f s y s z s ds with the given terminal condition y tau xi provided a certain integrability condition holds this result is applied to construct a continuous viscosity solution to the dirichlet problem for a class of semilinear elliptic pde s

stationary backward stochastic differential equations and associated partial differential equations by replacing the final condition for backward stochastic differential equations in short bsdes by a stationarity condition on the solution process we introduce a new class of bsdes in a natural manner we associate to such bsdes the periodic solution of second order partial differential equations with periodic structure

numerical stability analysis of the euler scheme for bsdes in this paper we study the qualitative behavior of approximation schemes for backward stochastic differential equations bsdes by introducing a new notion of numerical stability for the euler scheme we provide sufficient conditions in the one dimensional and multidimensional cases to guarantee the numerical stability we then perform a classical von neumann stability analysis in the case of a linear driver f and exhibit necessary conditions to get stability in this case finally we illustrate our results with numerical applications

ergodic control of semilinear stochastic equations and the hamilton jacobi equation abstract in this paper we consider optimal control of stochastic semilinear equations with lipschitz continuous drift and cylindrical noise we show existence and uniqueness up to an additive constant of solutions to the stationary hamilton jacobi equation associated with the cost functional given by the asymptotic average per unit time cost as a consequence we find the optimizing controls given in the feedback form to obtain these results we prove also some new results on the transition semigroups of semilinear diffusion acting in the spaces of continuous function with the weighted sup norms and on the optimal control of semilinear diffusions for the discounted cost functional

stochastic optimal control with delay in the control i solving the hjb equation through partial smoothing stochastic optimal control problems governed by delay equations with delay in the control are usually more difficult to study than those in which the delay appears only in the state this is particularly true when we look at the associated hamilton jacobi bellman hjb equation indeed even in the simplified setting introduced first by vinter and kwong siam j control optim 19 1981 pp 139 153 for the deterministic case the hjb equation is an infinite dimensional second order semilinear partial differential equation that does not satisfy the so called structure condition which substantially means that the control can act on the system modifying its dynamics at most along the same directions upon which the noise acts the absence of such a condition together with the lack of smoothing properties a common feature of problems with delay prevents the use of known techniques based on backward stochastic differential equations or on the smoothing properties of the linear part to prove the

ergodicity of robust switching control and nonlinear system of quasi variational inequalities we analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities these equations are related to robust switching control problems introduced in 3 we prove that as time horizon goes to infinity resp discount factor goes to zero the long run average solution to the parabolic system resp the limiting discounted solution to the elliptic system is characterized by a solution of a nonlinear system of ergodic variational inequalities our results hold under a dissipativity condition and without any non degeneracy assumption on the diffusion term our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities

second order hamilton jacobi equations in infinite dimensions some second order hamilton jacobi equations connected to stochastic optimal control problems for infinite dimensional systems driven by a white noise are studied a direct method to prove existence and uniqueness of mild solutions is developed then this solution is identified as the value function of the related stochastic control problem and a feedback formula for optimal controls is derived

the maximum principle for global solutions of stochastic stackelberg differential games national science foundation dms 1303775 research grant council of the hksar cityu 500113

the existence and uniqueness of the solution for nonlinear kolmogorov equations abstract by means of backward stochastic differential equations the existence and uniqueness of the mild solution are obtained for the nonlinear kolmogorov equations associated with stochastic delay evolution equations applications to optimal control are also given

stationary hamilton jacobi equations in hilbert spaces and applications to a stochastic optimal control problem we study an infinite horizon stochastic control problem associated with a class of stochastic reaction diffusion systems with coefficients having polynomial growth the hamiltonian is assumed to be only locally lipschitz continuous so that the quadratic case can be covered we prove that the value function v corresponding to the control problem is given by the solution of the stationary hamilton jacobi equation associated with the state system to this purpose we write the hamilton jacobi equation in integral form and by using the smoothing properties of the transition semigroup relative to the state system and the theory of m dissipative operators we show that it admits a unique solution moreover the value function v is obtained as the limit of minima for some approximating control problems which admit unique optimal controls and states

second order hamilton jacobi equations in hilbert spaces and stochastic boundary control the paper is concerned with fully nonlinear second order hamilton jacobi bellman isaacs equations of elliptic type in separable hilbert spaces which have unbounded first and second order terms the viscosity solution approach is adapted to the equations under consideration and the existence and uniqueness of viscosity solutions are proved a stochastic optimal control problem driven by a parabolic stochastic pde with control of dirichlet type on the boundary is considered it is proved that the value function of this problem is the unique viscosity solution of the associated hamilton jacobi bellman equation

diffusion semigroups in spaces of continuous functions with mixed topology abstract we study transition semigroups and kolmogorov equations corresponding to stochastic semilinear equations on a hilbert space h it is shown that the transition semigroup is strongly continuous and locally equicontinuous in the space of polynomially increasing continuous functions on h when endowed with the so called mixed topology as a result we characterize cores of certain second order differential operators in such spaces and show that they have unique extensions to generators of strongly continuous semigroups

infinite horizon bsdes with dissipative coefficients in hilbert spaces and applications in this paper we study a class of infinite horizon backward stochastic differential equations bsdes of the form dy t y t dt f t y t z t dt z t dw t 0 t in a real separable hilbert space where is a given real parameter and the coefficient f is dissipative in y and lipschitz in z by yosida approximation to dissipative mappings we show existence and uniqueness of the solutions for these equations this result is applied to construct unique viscosity solutions to semilinear elliptic partial differential equations pdes

large time behavior of solutions to semilinear equations with quadratic growth in the gradient this paper studies the large time behavior of solutions to semilinear cauchy problems with quadratic nonlinearity in gradients the cauchy problem considered has a general state space and may degenerate on the boundary of the state space two types of large time behavior are obtained i pointwise convergence of the solution and its gradient and ii convergence of solutions to associated backward stochastic differential equations when the state space is mathbb r d or the space of positive definite matrices both types of convergence are obtained under growth conditions on coefficients these large time convergence results have direct applications in risk sensitive control and long term portfolio choice problems

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

ergodic boundary point control of stochastic semilinear systems a controlled markov process in a hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain the linear term of the semilinear differential equation is the infinitesimal generator of an analytic semigroup the noise for the stochastic differential equation can be distributed boundary and point some ergodic properties of the controlled markov process are shown to be uniform in the control and the parameter the existence of an optimal control is verified to solve the ergodic control problem the optimal cost is shown to depend continuously on the system parameter

viability property for a backward stochastic differential equation and applications to partial differential equations in the present paper we study conditions under which the solutions of a backward stochastic differential equation remains in a given set of constraints this property is the so called viability property in a separate section this condition is translated to a class of partial differential equations

exponential stability of a mono tubular heat exchanger equation with output feedback abstract this paper is concerned with stability analysis of a mono tubular heat exchanger equation with static output feedback the mono tubular heat exchanger equation is exponentially stable when the input variable is identically zero in this paper it is shown that the c 0 semigroup generated by the closed loop operator consisting of the mono tubular heat exchanger equation and the output feedback law satisfies the spectrum determined growth assumption

on the existence of stochastic optimal control of distributed state system an optimal control problem governed by a semilinear parabolic stochastic differential equation with nonlinear diffusion coefficient is studied and the existence of a quasi optimal nonrelaxed control is proved without assuming convexity of the coefficients the control state space is not compact and of infinite dimension the stochastic equation is driven by a cylindrical brownian motion