internal stabilization of semilinear parabolic systems this work is concerned with the internal stabilization of the steady state solutions to semilinear parabolic systems via finite dimensional feedback controllers the internal controller is active on a nonempty open subset and in one equation only

stochastic bifurcation models we study an ordinary differential equation controlled by a stochastic process we present results on existence and uniqueness of solutions on associated local times trotter and ray knight theorems and on time and direction of bifurcation a relationship with lipschitz approximations to brownian paths is also discussed

a smooth nonparametric estimator of a quantile function abstract a smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed the proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile the mean squared convergence rate of the proposed estimator is also estimated monte carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator proposed by kaigh and lachenbruch the feasibility of using bootstrap techniques to estimate the optimal window width for the proposed estimator is also considered

on average cost stopping time problems we consider the stopping time problems whose costs are given by time average forms a generalization of the gittins index we show the existence of the optimal solutions and give their approximation to these stopping time problems

null controllability for the parabolic equation with a complex principal part abstract the paper is devoted to a study of the null controllability for the semilinear parabolic equation with a complex principal part for this purpose we establish a key weighted identity for partial differential operators i t j k 1 n k a j k j with real functions and by which we develop a universal approach based on global carleman estimate to deduce not only the desired explicit observability estimate for the linearized complex ginzburg landau equation but also all the known controllability observability results for the parabolic hyperbolic schrodinger and plate equations that are derived via carleman estimates

bandwidth selection for the smoothing of distribution functions summary several approaches can be made to the choice of bandwidth in the kernel smoothing of distribution functions recent proposals by sarda 1993 and by altman leger 1995 are analogues of the leave one out and plug in methods which have been widely used in density estimation in contrast a method of crossvalidation appropriate to the smoothing of distribution functions is proposed selection of the bandwidth parameter is based on unbiased estimation of a mean integrated squared error curve whose minimising value defines an optimal smoothing parameter this procedure is shown to lead to asymptotically optimal bandwidth choice not just in the usual first order sense but also in the second order sense in which kernel methods improve on the standard empirical distribution function some general theory on the performance of optimal data based methods of bandwidth choice is also provided leading to results which do not have analogues in the context of density estimation the numerical performances of all the methods discussed in the paper are compared a bandwidth based on a simple reference distribution is also included simulations suggest that the crossvalidatory proposal works well although the simple reference bandwidth is also quite effective

null boundary controllability of a one dimensional heat equation with an internal point mass and variable coefficients in this paper we consider a linear hybrid system which is composed by two non homogeneous rods connected by a point mass with dirichlet boundary conditions on the left end and a boundary control acts on the right end we prove that this system is null controllable with dirichlet or neumann boundary controls our approach is mainly based on a detailed spectral analysis together with the moment method in particular we show that the associated spectral gap in both cases dirichlet or neumann boundary controls is positive without further conditions on the coefficients other than the regularities

on the controllability of parabolic systems with a nonlinear term involving the state and the gradient we present some results concerning the controllability of a quasi linear parabolic equation with linear principal part in a bounded domain of mathbb r n with dirichlet boundary conditions we analyze the controllability problem with distributed controls supported on a small open subset and boundary controls supported on a small part of the boundary we prove that the system is null and approximately controllable at any time if the nonlinear term f y nabla y grows slower than y log 3 2 1 y nabla y nabla y log 1 2 1 y nabla y at infinity generally in this case in the absence of control blow up occurs the proofs use global carleman estimates parabolic regularity and the fixed point method

discrete multi armed bandits and multi parameter processes the general multi armed bandit problem is reformulated and solved as a control problem over a partially ordered set the approach taken provides a technically convenient framework for bandit like problems it also adds insight to the structure of strategies over partially ordered sets

optimal switching among several brownian motions for i 1 cdots d let b s i i be a one dimensional brownian motion on the interval 0 a i with absorption at the endpoints at each instant in time one must decide to run some subset of these d brownian motions while holding the others fixed at their current state the resulting process evolves in the rectangle d 0 a 1 times cdots times 0 a d if at some instant one decides to freeze all of the brownian motions then a reward is received in accordance with this final position two types of reward functions are considered first it is assumed that the reward is zero everywhere in d except along the d edges that correspond to the coordinate axes along these edges it is given by c 3 strictly concave functions gamma i x i which are zero at the endpoints 0 and a i of their domains the optimal control for this problem has a simple description let gamma i left x i right int 0 x i u gamma i u du and put m i left x in d gamma

a stochastic representation theorem with applications to optimization and obstacle problems we study a new type of representation problem for optional processes with connections to singular control optimal stopping and dynamic allocation problems as an application we show how to solve a variant of skorohod s obstacle problem in the context of backward stochastic differential equations

null controllability for a semilinear parabolic equation with gradient quadratic growth abstract this article is concerned with the null controllability of a semilinear parabolic equation with the nonlinear term involving the gradient quadratic term the technique in this paper is a combination of cole hopf transformation and some methods from a y khapalov controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term a qualitative approach siam j control optim 41 2003 1886 1900

optimal multiple stopping of linear diffusions motivated by the analysis of financial instruments with multiple exercise rights of american type and mean reverting underlyers we formulate and solve the optimal multiple stopping problem for a general linear regular diffusion process and a general reward function instead of relying on specific properties of geometric brownian motion and call and put option payoffs as in most of the existing literature we use general theory of optimal stopping for diffusions and we illustrate the resulting optimal exercise policies by concrete examples and constructive recipes

carleman estimates for a class of degenerate parabolic operators given alpha in 0 2 and f in l 2 0 t times 0 1 we derive new carleman estimates for the degenerate parabolic problem w t x alpha w x x f where t x in 0 t times 0 1 associated to the boundary conditions w t 1 0 and w t 0 0 if 0 leq alpha 1 or x alpha w x t 0 0 if 1 leq alpha 2 the proof is based on the choice of suitable weighted functions and hardy type inequalities as a consequence for all 0 leq alpha 2 and omega subset subset 0 1 we deduce null controllability results for the degenerate one dimensional heat equation u t x alpha u x x h chi omega with the same boundary conditions as above

on the controllability of the heat equation with nonlinear boundary fourier conditions in this paper we analyze the approximate and null controllability of the classical heat equation with nonlinear boundary conditions of the form y n f y 0 and distributed controls with support in a small set we show that when the function f is globally lipschitz continuous the system is approximately controllable we also show that the system is locally null controllable and null controllable for large time when f is regular enough and f 0 0 for the proofs of these assertions we use controllability results for similar linear problems and appropriate fixed point arguments in the case of the local and large time null controllability results the arguments are rather technical since they need among other things holder estimates for the control and the state

a note on recovering the distributions from exponential moments the problem of recovering a cumulative distribution function of a positive random variable via the scaled laplace transform inversion is studied the uniform upper bound of proposed approximation is derived the approximation of a compound poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound poisson distribution are investigated applying the simulation study the question of selecting the optimal scaling parameter of the proposed laplace transform inversion is considered the behavior of the approximants are demonstrated via plots and table

kernel quantile estimators abstract for an estimator of quantiles the efficiency of the sample quantile can be improved by considering linear combinations of order statistics that is l estimators a variety of such methods have appeared in the literature an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a guassian kernel and the bandwidths are identified it is seen that some implicit choices of the smoothing parameter are asymptotically suboptimal in addition the theory of this article suggests a method for choosing the smoothing parameter how much reliance should be placed on the theoretical results is investigated through a simulation study over a variety of distributions little consistent difference is found between various estimators an important conclusion made during the theoretical analysis is that all of these estimators usually provide only modest improvement over the sample quantile the results indicate that even if one knew the best estimator

stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation we consider the heat equation with a discontinuous diffusion coefficient and give uniqueness and stability results for both the diffusion coefficient and the initial condition from a measurement of the solution on an arbitrary part of the boundary and at some arbitrary positive time the key ingredient is the derivation of a carleman type estimate the diffusion coefficient is assumed to be discontinuous across an interface with a monotonicity condition

insensitizing controls for a phase field system abstract in this paper a nonlinear parabolic system modeling phase field phenomena is considered this system consists of two coupled parabolic equations the first one describes the temperature of the material and the second one describes a phase field function under small perturbations of the initial data we study the existence of controls insensitizing the phase field function and acting only on the temperature equation this problem is equivalent to the null controllability of a parabolic system which is studied by means of duality arguments carleman estimates and fixed point theorems

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

global carleman inequalities for parabolic systems and applications to controllability this paper has been conceived as an overview on the controllability properties of some relevant linear and nonlinear parabolic systems specifically we deal with the null controllability and the exact controllability to the trajectories we try to explain the role played by the observability inequalities in this context and the need of global carleman estimates we also recall the main ideas used to overcome the difficulties motivated by nonlinearities first we considered the classical heat equation with dirichlet conditions and distributed controls then we analyze recent extensions to other linear and semilinear parabolic systems and or boundary controls finally we review the controllability properties for the stokes and navier stokes equations that are known to date in this context we have paid special attention to obtaining the necessary carleman estimates some open questions are mentioned throughout the paper we hope that this unified presentation will be useful for those researchers interested in the field

remarks on the internal exponential stabilization to a nonstationary solution for 1d burgers equations the feedback stabilization of the burgers system to a nonstationary solution using finite dimensional internal controls is considered estimates for the dimension of the controller are derived in the particular case of no constraint on the support of the control a better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed some numerical examples are presented illustrating the stabilizing effect of the feedback control and suggesting that the existence of an estimate in the general case analogous to that in the particular one is plausible

carleman estimates for the one dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem abstract we study the observability and some of its consequences controllability identification of diffusion coefficients for one dimensional heat equations with discontinuous coefficients piecewise c 1 the observability for a linear equation is obtained by a carleman type estimate this kind of observability inequality yields controllability results for a semi linear equation as well as a stability result for the identification of the diffusion coefficient

an optimal stopping time problem with time average cost in a bounded interval abstract an optimal stopping time problem for a diffusion process stopped at the boundary of a bounded interval is studied our cost functional is of time average type which is different from standard long term average cost functional but can be considered as a version of the gittins index both characterization of the value function and construction of optimal stopping policy will be presented

continuous multi armed bandits and multiparameter processes a general framework is proposed for continuous time dynamic allocation models of a scarce resource among competing projects the allocation model is formulated as a multi armed bandit model and solved as a control problem of a multiparameter process in contrast to discrete time bandits where only one arm can be pulled at a time the continuous time bandit must allow simultaneous pulls the multiparameter approach allows a strong solution of diffusion type bandits here the main problem is to define precisely how to switch among arms and the solution involves local times

a probabilistic formula for the concave hull of a function let d be a compact convex domain in d dimensional euclidean space and let f be a nonnegative real valued function defined on d the classical optimal stopping problem is to find a stopping time that attains the supremum v x sup e x f b here b is a d dimensional brownian motion with absorption on the boundary of d and the supremum is over all stopping times it is well known that is characterized as the smallest superharmonic majorant of f in this paper we modify this problem by allowing b to be essentially any drift free diffusion with absorption as before on the boundary of d for example it could be a brownian motion diffusing on some lower dimensional affine set in addition one is allowed to switch among these diffusions at any time the problem is to find a stopping time and a switching strategy that together attain the supremum over all stopping times and all switching strategies for this problem we show that is characterized as the smallest concave majorant of f the domain d can be decomposed into a disjoint union of relatively open convex sets on each of which the function is affine furthermore the union of the zero dimensional convex sets is contained in the set on which f an optimal switching strategy is any strategy that at all times diffuses in the affine hull of the current convex set when the diffusion reaches the boundary of the current convex set it will lie on a lower dimensional convex set and must then diffuse on the affine hull of this new set this process continues until the set on which f is reached which is the optimal stopping time

jordan curves in the level sets of additive brownian motion keywords additive brownian motion brownian sheet level set jordan curve reference prob article 2001 002doi 10 1090 s0002 9947 01 02811 2view record in web of science record created on 2008 12 01 modified on 2017 05 12

null controllability of a class of newtonian filtration equations abstract in this paper we study the null controllability of a class of newtonian filtration equations using the properties of finite extinction time and finite speed of propagation we construct a control function in feedback form such that system is exactly null controllable at any time t 0 if we put a nonnegative constraint on the control function this system is not exactly null controllable any more but approximately null controllable for a long time

insensitizing controls for a heat equation with a nonlinear term involving the state and the gradient in this paper we present two results on the existence of insensitizing controls for a heat equation in a bounded domain of ir n we rst consider a semilinear heat equation involving gradient terms with homogeneous dirichlet boundary conditions then a heat equation with a nonlinear term f y and linear boundary conditions of fourier type is considered the nonlinearities are assumed to be globally lipschitz continuous in both cases we prove the existence of controls insensitizing the l 2 norm of the observation of the solution in an open subset o of the domain under suitable assumptions on the data each problem boils down to a special type of null controllability problem general observability inequalities are proved for linear systems similar to the linearized problem the proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate xed point arguments

approximate controllability of the semilinear heat equation this article is concerned with the study of approximate controllability for the semilinear heat equation in a bounded domain when the control acts on any open and nonempty subset of or on a part of the boundary in the case of both an internal and a boundary control the approximate controllability in l p for 1 p l in the case of the interior control we also prove approximate controllability in c 0 the proof combines a variational approach to the controllability problem for linear equations and a fixed point method we also prove that the control can be taken to be of quasi bang bang form

recovery of ruin probability and value at risk from the scaled laplace transform inversion abstract in this paper we propose three modified approximations of the ruin probability and the inverse function of the ruin probability using the inversion of the scaled values of laplace transform suggested by mnatsakanov et al 2015 the problem of evaluating numerically the tail value at risk of an insurance portfolio is also discussed briefly performances of the proposed constructions are demonstrated via the graphs and tables using several examples

local controllability of multidimensional quasi linear parabolic equations this paper studies the local controllability for a class of multidimensional quasi linear parabolic equations with homogenous dirichlet boundary conditions and an arbitrarily located internal controller unlike the known result in one spacial dimension controllability is analyzed in the frame of classical solutions the key of our approach is to seek a control function in the holder space for given data with certain regularity in order to give the cost estimate for the control function we establish an observability inequality for linear parabolic equations with an explicit estimate on the observability constant in terms of the c 1 coefficients of principal parts the later is based on a new global carleman estimate for general linear parabolic equations which has an independent interest

carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations in a bounded domain of r n 1 n geq 2 we consider a second order elliptic operator a d x 0 2 nabla x cdot c x nabla x where the scalar coefficient c x is piecewise smooth yet discontinuous across a smooth interface s we prove a local carleman estimate for a in the nhd of any point of the interface the observation region can be chosen independently of the sign of the jump of the coefficient c at the considered point the derivation of this estimate relies on the separation of the problem into three microlocal regions and the calderon projector technique following the method of lebeau and robbiano cite lr 95 we then prove the null controllability for the linear parabolic initial problem with dirichlet boundary conditions associated to the operator d t nabla x cdot c x nabla x

the hausdorff entropic moment problem our aim in this paper is twofold first to find the necessary and sufficient conditions to be satisfied by a given sequence of real numbers n n 0 to represent the entropic moments 0 a x ndx of an unknown non negative decreasing and differentiable a e density function x with a finite interval support these moments are called entropic moments because they are closely connected with various information entropies renyi tsallis second we outline an efficient method for the reconstruction of the density function from the knowledge of its first n entropic moments

recovery of a quantile function from moments the problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its laplace transform is studied two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed the uniform and l 1 upper bounds of proposed estimates are derived the plots illustrate the behavior of the recovered approximants for the moderate and large sample sizes

local and global carleman estimates for parabolic operators with coefficients with jumps at interfaces in 0 t open subset of n n 2 we consider a parabolic operator p t x t x x where the scalar coefficient t x is piecewise smooth in space yet discontinuous across a smooth interface s we prove a global in time local in space carleman estimate for p in the neighborhood of any point of the interface the observation region can be chosen independently of the sign of the jump of the coefficient at the considered point the derivation of this estimate relies on the separation of the problem into three microlocal regions related to high and low tangential frequencies at the interface in the high frequency regime we use calderon projectors in the low frequency regime we follow a more classical approach because of the parabolic nature of the problem we need to introduce weyl hormander anisotropic metrics symbol classes and pseudo differential operators each frequency regime and the associated technique require a different calculus a global in time and space carleman estimate on 0 t m m a manifold is also derived from the local result

two parameter optimal stopping and bi markov processes in this paper the optimal stopping problem is solved for particular two parameter processes here called bi markov processes a subsequent potential theory is developed with respect to a pair of one parameter semi groups we introduce a new notion of harmonicity for two variable functions and we interpret it in the framework of the theory of bi markov processes

theoretical and numerical local null controllability for a parabolic system with local and nonlocal nonlinearities this paper deals with the null controllability of an initial boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds the control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small we first prove that if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition the equations can be driven exactly to zero we also present an iterative algorithm of the quasi newton kind for the computation of the control and we prove a convergence result the behavior of this algorithm is illustrated with some numerical experiments

on the moment recovered approximations of regression and derivative functions with applications in this paper three formulas for recovering the conditional mean and conditional variance based on product moments are proposed the upper bounds for the uniform rate of approximations of regression and derivatives of some moment determinate function are derived two cases where the support of underlying functions is bounded and unbounded from above are studied based on the proposed approximations novel nonparametric estimates of the distribution function and its density in multiplicative censoring model are constructed simulation study justifies the consistency of the estimates

two armed restless bandits with imperfect information stochastic control and indexability we present a two armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm these dynamics are natural in applications such as human capital development job search and occupational choice using new insights from stochastic control along with a monotonicity condition on the payoff dynamics we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with gittins index our result implies the indexability of a new class of restless bandit models

null controllability of a parabolic equation involving the grushin operator in some multi dimensional domains abstract we study the null controllability of the linear parabolic equation involving the grushin operator g s x x 2 s y s 0 in the domain 1 1 n 1 0 1 n 2 r n 1 r n 2 n 1 n 2 1 under an additive control supported in an open subset of we prove that the equation is null controllable in any positive time for s 1 and not null controllable for s 1 when s 1 a positive minimal time is required for null controllability

time optimal control of semilinear parabolic equations via bilinear controls abstract we establish the existence of the time optimal control for semilinear parabolic equations with gradient quadratic growth via bilinear controls it is worth pointing out that there is no restriction on the growth of the nonlinearity f s with respect to the variable s in the equation which is a remarkable difference compared to the semilinear parabolic system with locally distributed controls the technique used in this paper is the combination of the hopf cole transformation the a prior estimates on solutions of parabolic equations and the strategy of the stepwise control

carleman estimates for stratified media abstract we consider anisotropic elliptic and parabolic operators in a bounded stratified media in r n characterized by discontinuities of the coefficients in one direction the surfaces of discontinuities cross the boundary of the domain we prove carleman estimates for these operators with an arbitrary observation region

null controllability of semilinear parabolic equation with nonlinear terms involving a maximal monotone graph this work concerns the null controllability of the system governed by semilinear parabolic equation with nonlinearity involving a bounded maximal monotone graph we obtain by the kakutani s fixed point theorem and the associated controllability for linear parabolic equations that the system is null controllable in the case when control acts in a subdomain as a consequence we also obtain that the system is null controllable when control acts on a portion of the boundary

on the optimal reward function of the continuous time multiarmed bandit problem the optimal reward function associated with the so called multiarmed bandit problem for general markov feller processes is considered it is shown that this optimal reward function has a simple expression product form in terms of individual stopping problems without any smoothness properties of the optimal reward function neither for the global problem nor for the individual stopping problems some results relative to a related problem with switching cost are obtained

l infty null controllability for the heat equation and its consequences for the time optimal control problem in this paper we establish a certain l infty null controllability for the internally controlled heat equation in omega times 0 t with the control restricted to a product set of an open nonempty subset in omega and a subset of positive measure in the interval 0 t based on this we obtain a bang bang principle for the time optimal control of the heat equation with controls taken from the set mathcal u ad u cdot t 0 infty rightarrow l 2 omega measurable u cdot t in u a e in t where u is a closed and bounded subset of l 2 omega namely each optimal control u cdot t of the problem satisfies necessarily the bang bang property u cdot t in partial u for almost all t in 0 t where partial u denotes the boundary of the set u and t is the optimal time we also get the uniqueness of the optimal control when the target set s is convex and the control set u is a closed ball

null controllability for a parabolic equation with nonlocal nonlinearities abstract in this paper we establish a local null controllability result for a nonlinear parabolic pde with nonlocal nonlinearities the result relies on the global null controllability of similar linear equations and a fixed point argument we also analyze other similar controllability problems and we present several open questions

a martingale approach to minimal surfaces abstract we provide a probabilistic approach to studying minimal surfaces in r 3 after a discussion of the basic relationship between brownian motion on a surface and minimality of the surface we introduce a way of coupling brownian motions on two minimal surfaces this coupling is then used to study two classes of results in minimal surface theory maximum principle type results such as weak and strong halfspace theorems and the maximum principle at infinity and liouville theorems

carleman estimates and controllability results for the one dimensional heat equation with bv coefficients abstract we derive global carleman estimates for one dimensional linear parabolic equations t x c x with a coefficient of bounded variations these estimates are obtained by approximating c by piecewise constant coefficients c e and passing to the limit in the carleman estimates associated to the operators defined with c e such estimates yields observability inequalities for the considered linear parabolic equation which in turn yield controllability results for classes of semilinear equations

bandit problems with levy processes bandit problems model the trade off between exploration and exploitation in various decision problems we study two armed bandit problems in continuous time where the risky arm can have two types high or low both types yield stochastic payoffs generated by a levy process we show that the optimal strategy is a cut off strategy and we provide an explicit expression for the cut off and for the optimal payoff

on the controllability of a free boundary problem for the 1d heat equation abstract this paper deals with the local null control of a free boundary problem for the classical 1d heat equation with distributed controls locally supported in space in the main result we prove that if the final time t is fixed and the initial state is sufficiently small there exist controls that drive the state exactly to rest at time t t

on a class of non linear parabolic control systems with memory effects this work establishes the local exact null controllability of non linear parabolic integrodifferential equations with non linearities under the integral sign in a bounded domain and with homogeneous dirichlet boundary conditions the control is assumed to be distributed along a subdomain of using a carleman type inequality we first prove the global exact null controllability of a linearized equation then by a fixed point method we obtain the main result for the non linear case this result asserts that when the non linearity is of class c 1 and globally lipschitz the system is null controllable

on the null controllability of heat equation with memory abstract the aim of this article is to analyze the null controllability properties of the heat equations with memory by a new carleman inequality with weighted functions that do not vanish at t 0 we prove the controllability for the system with a located internal controller under a condition on the kernel

controllability for parabolic equations with nonlinear memory this paper is concerned with the controllability of a parabolic system with nonlinear memory based on the localized estimate of the solution we prove that the system with a superlinear growth memory is not controllable furthermore two controllability results for some initial data and targets are given as well

optimal switching between a pair of brownian motions consider two brownian motions b 1 s1 and b 2 s2 each taking values on an interval 0 a i i 1 2 with absorption at the endpoints we can alternate between letting b 1 s1 run while freezing b 2 s2 and letting b 2 s2 run while freezing b 1 s1 this results in a swtiched process that evolves in the rectangle d 0 a 1 0 a 2 like a horizontal brownian motion when b 2 s2 freezes and like a vertical brownian motion when b 1 s1 freezes let f x 1 x 2 be a nonnegative continuous payoff function defined on the boundary d of d a control consists of a switching strategy and a stopping time we study the problem of finding an optimal control which maximizes the expected payoff obtained at time stopping in the interior results in zero reward

null controllability of some reaction diffusion systems with one control force this work is concerned with the null controllability of semilinear parabolic systems by a single control force acting on a subdomain

boundary controllability of a one dimensional phase field system with one control force abstract in this paper we present some controllability results for linear and nonlinear phase field systems of caginalp type considered in a bounded interval of r when the scalar control force acts on the temperature equation of the system by means of the dirichlet condition on one of the endpoints of the interval in order to prove the linear result we use the moment method providing an estimate of the cost of fast controls using this estimate and following the methodology developed in 19 we prove a local exact boundary controllability result to constant trajectories of the nonlinear phase field system to the authors knowledge this is the first nonlinear boundary controllability result in the framework of non scalar parabolic systems framework in which some hyperbolic behaviors could arise