inconsistent estimation and asymptotically equal interpolations in model based geostatistics it is shown that in model based geostatistics not all parameters in the matern class can be estimated consistently if data are observed in an increasing density in a fixed domain regardless of the estimation methods used nevertheless one quantity can be estimated consistently by the maximum likelihood method and this quantity is more important to spatial interpolation the results are established by using the properties of equivalence and orthogonality of probability measures some sufficient conditions are provided for both gaussian and non gaussian equivalent measures and necessary conditions are provided for gaussian equivalent measures two simulation studies are presented that show that the fixed domain asymptotic properties can explain some finite sample behavior of both interpolation and estimation when the sample size is moderately large

on gevrey regularity of the supercritical sqg equation in critical besov spaces abstract in this paper we show that the solution of the supercritical surface quasi geostrophic sqg equation with initial data in a critical besov space belongs to a subanalytic gevrey class in order to prove this a suitable estimate on the nonlinear term in the form of a commutator is required we express the commutator as a bilinear multiplier operator and obtain single scale estimates for its symbol in particular we show that the localized symbol is of marcinkiewicz type and show that due to the localizations inherited from working in the besov spaces this condition implies the requisite boundedness of the corresponding operator this result strengthens previous ones which showed that solutions starting from initial data in critical besov spaces are classical as a direct consequence of our method decay estimates of higher order derivatives are easily deduced

generalized surface quasi geostrophic equations with singular velocities this paper establishes several existence and uniqueness results for two families of active scalar equations with velocity fields determined by the scalars through very singular integrals the first family is a generalized surface quasigeostrophic sqg equation with the velocity field u related to the scalar by where and is the zygmund operator the borderline case 1 corresponds to the sqg equation and the situation is more singular for 1 we obtain the local existence and uniqueness of classical solutions the global existence of weak solutions and the local existence of patch type solutions the second family is a dissipative active scalar equation with which is at least logarithmically more singular than the velocity in the first family we prove that this family with any fractional dissipation possesses a unique local smooth solution for any given smooth data this result for the second family constitutes a first step towards resolving the global regularity issue recently proposed by k ohkitani 2012 wiley periodicals inc

on global regularity of 2d generalized magnetohydrodynamic equations abstract in this article we study the global regularity of 2d generalized magnetohydrodynamic equations 2d gmhd in which the dissipation terms are u and b we show that smooth solutions are global in the following three cases 1 2 1 0 1 2 2 2 2 0 we also show that in the inviscid case 0 if 1 then smooth solutions are global as long as the direction of the magnetic field remains smooth enough

computer model calibration using high dimensional output this work focuses on combining observations from field experiments with detailed computer simulations of a physical process to carry out statistical inference of particular interest here is determining uncertainty in resulting predictions this typically involves calibration of parameters in the computer simulator as well as accounting for inadequate physics in the simulator the problem is complicated by the fact that simulation code is sufficiently demanding that only a limited number of simulations can be carried out we consider applications in characterizing material properties for which the field data and the simulator output are highly multivariate for example the experimental data and simulation output may be an image or may describe the shape of a physical object we make use of the basic framework of kennedy and o hagan however the size and multivariate nature of the data lead to computational challenges in implementing the framework to overcome these challenges we make use of basis repre

the well posedness of the surface quasi geostrophic equations in the besov morrey spaces abstract in this paper we develop the boundedness of riesz transform in morrey spaces which generalize the corresponding result in the usual l p spaces as an application of this boundedness we establish the well posedness and blow up criterion for the surface quasi geostrophic equations in the framework of besov morrey spaces

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

local and global solvability and blow up for the drift diffusion equation with the fractional dissipation in the critical space abstract we study local and global existence and uniqueness of solutions to the drift diffusion equation with fractional dissipation 2 in the preceding works for some associated equations the cases 1 and 1 are known as critical and supercritical respectively in the critical and supercritical cases we may not apply the l p theory for semilinear equations of parabolic type used in the subcritical case 1 2 we discuss local existence with large data and global existence with small data in the besov space b p q n p r n which corresponds to the scaling invariant space of the equation furthermore we show that solutions can blow up in finite time if initial data is not small

dissipative quasi geostrophic equation for large initial data in the critical sobolev space the critical and super critical dissipative quasi geostrophic equations are investigated in mathbb r 2 we prove local existence of a unique regular solution for arbitrary initial data in h2 2 which corresponds to the scaling invariant space of the equation we also consider the behavior of the solution near t 0 in the sobolev space

on the quasi geostrophic equations on compact closed surfaces in r3 abstract the quasi geostrophic equations on compact surfaces in r 3 without boundary are studied by means of the theory of quasi linear parabolic evolution equations based on maximal l p regularity it is shown that the problem is globally strongly well posed in l q the solutions regularize instantly and form a global semiflow in the proper state manifold and as time goes to infinity a solution converges exponentially to a constant in the topology of the state space

global well posedness for the critical 2d dissipative quasi geostrophic equation we give an elementary proof of the global well posedness for the critical 2d dissipative quasi geostrophic equation the argument is based on a non local maximum principle involving appropriate moduli of continuity

indefinite mean field stochastic linear quadratic optimal control this paper is concerned with the discrete time indefinite mean field linear quadratic optimal control problem the so called mean field type stochastic control problems refer to the problem of incorporating the means of the state variables into the state equations and cost functionals such as the mean variance portfolio selection problems a dynamic optimization problem is called to be nonseparable in the sense of dynamic programming if it is not decomposable by a stage wise backward recursion the classical dynamic programming based optimal stochastic control methods would fail in such nonseparable situations as the principle of optimality no longer applies in this paper we show that both the well posedness and the solvability of the indefinite mean field linear quadratic problem are equivalent to the solvability of two coupled constrained generalized difference riccati equations and a constrained linear recursive equation we characterize the optimal control set completely and obtain a set of necessary and sufficient conditions on the mean variance portfolio selection problem the results established in this paper offer a more accurate solution scheme in tackling directly the issue of nonseparability and deriving the optimal policies analytically for the mean variance type portfolio selection problems

a new bernstein s inequality and the 2d dissipative quasi geostrophic equation we show a new bernstein s inequality which generalizes the results of cannone planchon danchin and lemarie rieusset as an application of this inequality we prove the global well posedness of the 2d quasi geostrophic equation with the critical and super critical dissipation for the small initial data in the critical besov space and local well posedness for the large initial data

linear quadratic risk sensitive and robust mean field games this paper considers two classes of large population stochastic differential games connected to optimal and robust decentralized control of large scale multiagent systems the first problem p1 is one where each agent minimizes an exponentiated cost function capturing risk sensitive behavior whereas in the second problem p2 each agent minimizes a worst case risk neutral cost function where the worst case stems from the presence of an adversary entering each agent s dynamics characterized by a stochastic differential equation in both problems the individual agents are coupled through the mean field term included in each agent s cost function which captures the average or mass behavior of the agents we solve both p1 and p2 via mean field game theory specifically we first solve a generic risk sensitive optimal control problem and a generic stochastic zero sum differential game where the corresponding optimal controllers are applied by each agent to construct the mean field systems of p1 and p2 we then characterize an approximated mass behavior effect on an individual agent via a fixed point analysis of the mean field system for each problem p1 and p2 we show that the approximated mass behavior is in fact the best estimate of the actual mass behavior in various senses as the population size n goes to infinity moreover we show that for finite n there exist epsilon nash equilibria for both p1 and p2 where the corresponding individual nash strategies are decentralized in terms of local state information and the approximated mass behavior we also show that epsilon can be taken to be arbitrarily small when n is sufficiently large we show that the epsilon nash equilibria of p1 and p2 are partially equivalent in the sense that the individual nash strategies share identical control laws but the approximated mass behaviors for p1 and p2 are different since in p2 the mass behavior is also affected by the associated worst case disturbance finally we prove that the nash equilibria for p1 and p2 both feature robustness and as the parameter characterizing this robustness becomes infinite the two nash equilibria become identical and equivalent to that of the risk neutral case as in the one agent risk sensitive and robust control theory

linear quadratic optimal control problems for mean field stochastic differential equations linear quadratic optimal control problems are considered for mean field stochastic differential equations with deterministic coefficients by a variational method the optimality system is derived which is a linear mean field forward backward stochastic differential equation using a decoupling technique two riccati differential equations are obtained which are uniquely solvable under certain conditions then a feedback representation is obtained for the optimal control

regularity criteria for the dissipative quasi geostrophic equations in holder spaces we study regularity criteria for weak solutions of the dissipative quasi geostrophic equation with dissipation 2 0 1 we show in this paper that if theta in c 0 t c 1 gamma or theta in l r 0 t c alpha with alpha 1 gamma frac gamma r is a weak solution of the 2d quasi geostrophic equation then is a classical solution in 0 t times mathbb r 2 this result improves our previous result in 18

global well posedness in the super critical dissipative quasi geostrophic equations we consider the quasi geostrophic equation with the dissipation term in the case constantin cordoba wu 6 proved the global existence of strong solution in h 1 and h 2 under the assumption of small l norm of initial data in this paper we prove the global existence in the scale invariant besov space b 2 2 2 1 for initial data small in the b 2 2 2 1 norm we also prove a global stability result in b 1 2 1

linear exponential quadratic gaussian control in this technical note an optimal control problem for a linear stochastic system with brownian motion and a cost that is an exponential of a quadratic functional of the state and the control is solved by obtaining explicitly an optimal control and the optimal cost while this solution has been previously obtained the approach given here is direct and elementary and does not use the well known solution methods of the hamilton jacobi bellman equation or the stochastic maximum principle the approach given here presents a basic insight in the solution by providing a simple explanation for the additional term in the riccati equation for the optimal control as compared to the riccati equation for the linear quadratic gaussian control problem

mean field stochastic h 2 h control with delay the finite horizon h 2 h control problem of mean field type for delayed stochastic systems is considered in this paper firstly we derive a sufficient mean field generalised stochastic bounded

risk sensitive zero sum differential games we consider two player risk sensitive zero sum differential games rszsdgs in our problem setup both the drift term and the diffusion term in the controlled stochastic differential equation are dependent on the state and controls of both players and the objective functional is of the risk sensitive type first a stochastic maximum principle type necessary condition for an open loop saddle point of the rszsdg is established via nonlinear transformations of the adjoint processes of the equivalent risk neutral stochastic zero sum differential game in particular we obtain two variational inequalities namely the pair of saddle point inequalities of the rszsdg next we obtain the hamilton jacobi isaacs partial differential equation for the rszsdg which provides a sufficient condition for a feedback saddle point of the rszsdg using a logarithmic transformation of the associated value function finally we study the extended linear quadratic rszsdg lq rszsdg we show intractability of the extended lq rszsdg with the state and or controls of both players appearing in the diffusion term this unexpected intractability could lead to nonlinear open loop and feedback saddle points even if the problem itself is essentially lq and the isaacs condition holds

estimating ocean circulation an mcmc approach with approximated likelihoods via the bernoulli factory we provide a bayesian analysis of ocean circulation based on data collected in the south atlantic ocean the analysis incorporates a reaction diffusion partial differential equation that is not solvable in closed form this leads to an intractable likelihood function we describe a novel markov chain monte carlo approach that does not require a likelihood evaluation rather we use unbiased estimates of the likelihood and a bernoulli factory to decide whether or not proposed states are accepted the variates required to estimate the likelihood function are obtained via a feynman kac representation this lifts the common restriction of selecting a regular grid for the physical model and eliminates the need for data preprocessing we implement our approach using the parallel graphic processing unit gpu computing environment

mean field stochastic linear quadratic optimal control with markov jump parameters abstract this paper considers a class of mean field stochastic linear quadratic optimal control problems with markov jump parameters the new feature of these problems is that means of state and control are incorporated into the systems and the cost functional based on the modes of markov chain the corresponding decomposition technique of augmented state and control is introduced it is shown that under some appropriate conditions there exists a unique optimal control which can be explicitly given via solutions of two generalized difference riccati equations a numerical example sheds light on the theoretical results established

commutator estimate in terms of partial derivatives of solutions for the dissipative quasi geostrophic equation through littlewood paley decomposition argument a commutator estimate in terms of partial derivatives of solutions for the critical and supercritical dissipative 2d quasi geostrophic equation is established as an application of this estimate we obtain some new a priori estimates and prove the existence and uniqueness of solution for the small initial data in critical besov spaces

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

linear quadratic mean field stochastic zero sum differential games abstract in this paper we consider the two player linear quadratic mean field stochastic differential game lq mf szsdg where the expected values of state and players control variables are included in the corresponding mean field stochastic system and the objective functional we characterize the explicit condition under which the feedback saddle point equilibrium for the lq mf szsdg exists the results are obtained by using the completion of squares method and the ordered interchangeability property of multiple saddle points we show that the corresponding saddle point equilibrium is linear in state which is characterized by the two coupled riccati differential equations crdes we also discuss the solvability conditions of the crdes numerical results are presented to verify the theoretical results of the paper

drift diffusion equations with fractional diffusion and the quasi geostrophic equation motivated by the critical dissipative quasi geostrophic equation we prove that drift diffusion equations with l 2 initial data and minimal assumptions on the drift are locally holder continuous as an application we show that solutions of the quasi geostrophic equation with initial l 2 data and critical diffusion 1 2 are locally smooth for any space dimension

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

linear exponential quadratic control for mean field stochastic systems in this technical note we consider linear exponential quadratic leq control for mean field stochastic differential equations mfsdes the mfsde includes the expectation value of state and control and the objective functional is exponential of a quadratic functional in state control and their expectations we obtain the explicit optimal solution as well as the optimal cost the corresponding optimal solution is linear in state and its expectation which is characterized by the riccati differential equations rdes the results are obtained by showing that after applying the completion of squares method the remaining exponentiated stochastic integral and additional rde terms can be eliminated together by taking expectation since they constitute the associated radon nikodym derivative as an extension of the problem the leq zero sum differential game is considered for which we obtain the explicit optimal solution saddle point equilibrium as well as the optimal cost

gevrey regularity for the supercritical quasi geostrophic equation abstract in this paper following the techniques of foias and temam we establish suitable gevrey class regularity of solutions to the supercritical quasi geostrophic equations in the whole space with initial data in critical sobolev spaces moreover the gevrey class that we obtain is near optimal and as a corollary we obtain temporal decay rates of higher order sobolev norms of the solutions unlike the navier stokes or the subcritical quasi geostrophic equations the low dissipation poses a difficulty in establishing gevrey regularity a new commutator estimate in gevrey classes involving the dyadic littlewood paley operators is established that allow us to exploit the cancellation properties of the equation and circumvent this difficulty

a new risk sensitive maximum principle in this paper a new maximum principle for the risk sensitive control problem is established one important feature of this result is that it applies to systems in which the diffusion term may depend on the control such control dependence gives rise to interesting phenomena not observed in the usual setting where control independence of the diffusion term is assumed in particular there is an additional second order adjoint equation and additional terms in the maximum condition that involve this second order process as well as the risk sensitive parameter moreover contrary to a conventional maximum principle the first order adjoint equation involved in our maximum principle is a nonlinear equation an advantage of considering this new type of adjoint equation is that the risk sensitive maximum principle derived is similar in form to its risk neutral counterpart the approach is based on the logarithmic transformation and the relationship between the adjoint variables and the value function as an example a linear quadratic risk sensitive problem is solved using the maximum principle derived

information rates of nonparametric gaussian process methods we consider the quality of learning a response function by a nonparametric bayesian approach using a gaussian process gp prior on the response function we upper bound the quadratic risk of the learning procedure which in turn is an upper bound on the kullback leibler information between the predictive and true data distribution the upper bound is expressed in small ball probabilities and concentration measures of the gp prior we illustrate the computation of the upper bound for the matern and squared exponential kernels for these priors the risk and hence the information criterion tends to zero for all continuous response functions however the rate at which this happens depends on the combination of true response function and gaussian prior and is expressible in a certain concentration function in particular the results show that for good performance the regularity of the gp prior should match the regularity of the unknown response function

loss function approaches to predict a spatial quantile and its exceedance region in the analysis of spatial data it is common to predict a spatial exceedance and its associated exceedance region this is scientifically important because unusual events tend to strongly affect the environment we use classes of loss functions based on image metrics e g baddeley s loss function to predict the spatial exceedance region we then propose a joint loss to predict a spatial quantile and its exceedance region the optimal predictor is obtained by minimizing the posterior expected loss given the process parameters which we achieve by simulated annealing various predictors are compared through simulation this methodology is applied to a spatial data set of temperature change over the americas

maximum likelihood estimation for stochastic differential equations using sequential gaussian process based optimization abstractstochastic differential equations sdes are used as statistical models in many disciplines however intractable likelihood functions for sdes make inference challenging and we need to resort to simulation based techniques to estimate and maximize the likelihood function while importance sampling methods have allowed for the accurate evaluation of likelihoods at fixed parameter values there is still a question of how to find the maximum likelihood estimate in this article we propose an efficient gaussian process based method for exploring the parameter space using estimates of the likelihood from an importance sampler our technique accounts for the inherent monte carlo variability of the estimated likelihood and does not require knowledge of gradients the procedure adds potential parameter values by maximizing the so called expected improvement leveraging the fact that the likelihood function is assumed to be smooth our simulations demonstrate that our method has significant computation

linear exponential quadratic stochastic differential games in this technical note a two person noncooperative stochastic differential game described by a linear stochastic equation with a brownian motion and a payoff that is the exponential of a quadratic functional in the state and the control strategies of the two players is explicitly solved the optimal strategies form a nash equilibrium the value of the game is also determined explicitly the solution of this problem is naturally related to a linear quadratic stochastic differential game and a linear exponential quadratic control problem

a pointwise estimate for fractionary derivatives with applications to partial differential equations this article emphasizes the role played by a remarkable pointwise inequality satisfied by fractionary derivatives in order to obtain maximum principles and lp decay of solutions of several interesting partial differential equations in particular there are applications to quasigeostrophic flows in two space variables with critical viscosity that model the eckman pumping see baroud ch n plapp b b she z s swinney h l 2002 phys rev lett 88 114501 and constantin p 2002 phys rev lett 89 184501

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

global cauchy problem of 2d generalized magnetohydrodynamic equations abstract in this paper we prove the global in time existence of smooth solutions of the 2d generalized magnetohydrodynamic equations with zero viscosity when the power of the laplacian operator in the dissipation term of the induction equation is between 1 and 2 we also show a regularity criterion on the direction of the magnetic field b 0 b b when 1

existence and uniqueness results for the 2 d dissipative quasi geostrophic equation abstract this paper concerns itself with besov space solutions of the 2 d quasi geostrophic qg equation with dissipation induced by a fractional laplacian the goal is threefold first to extend a previous result on solutions in the inhomogeneous besov space b 2 q r j wu global solutions of the 2d dissipative quasi geostrophic equation in besov spaces siam j math anal 36 2004 2005 1014 1030 to cover the case when r 2 2 second to establish the global existence of solutions in the homogeneous besov space b p q r with general indices p and q and third to determine the uniqueness of solutions in any one of the four spaces b 2 q s b p q r l q 0 t b 2 q s 2 q and l q 0 t b p q r 2 q where s 2 2 and r 1 2 2 p

a stochastic maximum principle for delayed mean field stochastic differential equations and its applications in this technical note we discuss the stochastic optimal control problems of mean field stochastic differential delayed equations mfsddes which arise naturally from various backgrounds including economics finance engineering and physics etc to this end some new estimates are used to handle the complex structure of our controlled system due to the presence of both delay and mean field characters as the main result a stochastic maximum principle for the mean field stochastic optimal control with delay mfsocd is derived in terms of necessary and sufficient conditions in particular applying the convex variation and duality relation we obtain the necessary condition for optimality see theorem 1 in addition the sufficient condition of the optimality is also obtained under some convex condition see theorem 2 based on our maximum principle the related mean field linear quadratic delayed mflqd optimal control problems are also investigated the optimal control is derived and its existence is also verified refer theorem 3 as illustration an example is also proposed and its explicit optimal control is derived

risk sensitive mean field games in this paper we study a class of risk sensitive mean field stochastic differential games we show that under appropriate regularity conditions the mean field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a hamilton jacobi bellman hjb equation with an additional quadratic term we provide an explicit solution of the mean field best response when the instantaneous cost functions are log quadratic and the state dynamics are affine in the control an equivalent mean field risk neutral problem is formulated and the corresponding mean field equilibria are characterized in terms of backward forward macroscopic mckean vlasov equations fokker planck kolmogorov equations and hjb equations we provide numerical examples on the mean field behavior to illustrate both linear and mckean vlasov dynamics

on the 2d critical and supercritical dissipative quasi geostrophic equation in besov spaces abstract we prove the local smoothing effect of the 2d critical and supercritical dissipative quasi geostrophic equations in critical besov spaces as an application a global well posedness result is established by adapting a method in kiselev nazarov and volberg 2007 16 and an idea in dong and du 2008 15 with suitable modifications moreover we show that the unique solution obtained in chen miao and zhang 2007 11 is a classical solution these generalize some previous results in dong 2010 13 dong and du 2008 15 the main ingredients of the proofs are two commutator estimates and the preservation of suitable modulus of continuity of the solutions

remarks on the breakdown of smooth solutions for the 3 d euler equations the authors prove that the maximum norm of the vorticity controls the breakdown of smooth solutions of the 3 d euler equations in other words if a solution of the euler equations is initially smooth and loses its regularity at some later time then the maximum vorticity necessarily grows without bound as the critical time approaches equivalently if the vorticity remains bounded a smooth solution persists

the risk sensitive maximum principle for controlled forward backward stochastic differential equations abstract in this paper we consider the risk sensitive optimal control problem for forward backward stochastic differential equations fbsdes we consider two different cases case 1 the drift and diffusion terms of the forward part are independent of the backward part not fully coupled fbsde and the running cost does not include the backward part case 2 the fully coupled fbsde with terminal and initial costs in both cases the risk sensitive objective functional is considered the corresponding control domain is not necessarily convex and the diffusion term of the forward part depends on control and state variables in both cases by using the nonlinear transformations of the equivalent risk neutral problems we obtain two different risk sensitive maximum principles which are characterized in terms of the variational inequalities we show that the risk sensitive maximum principle of case 1 consists of the two coupled adjoint equations with an additional scalar adjoint equation which are backward stochastic differential equations bsdes the risk sensitive maximum principle of case 2 consists of the two coupled adjoint equations which are coupled fbsdes with an additional scalar adjoint equation and optimality conditions in both cases the additional scalar adjoint equations are bsdes which are induced due to the nonlinear transformations of the adjoint processes in the equivalent risk neutral problems through the application of results we consider the linear quadratic risk sensitive optimal control problem for the linear fbsde and by using the risk sensitive maximum principle of case 1 we characterize an explicit optimal solution

bayesian calibration of computer models we consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models such models implemented as computer codes are often generic in the sense that by a suitable choice of some of the model s input parameters the code can be used to predict the behaviour of the system in a variety of specific applications however in any specific application the values of necessary parameters may be unknown in this case physical observations of the system in the specific context are used to learn about the unknown parameters the process of fitting the model to the observed data by adjusting the parameters is known as calibration calibration is typically effected by ad hoc fitting and after calibration the model is used with the fitted input values to predict the future behaviour of the system we present a bayesian calibration technique which improves on this traditional approach in two respects first the predictions allow for all sources of uncertainty including the remaining uncertainty over the fitted parameters second they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best fitting parameter values the method is illustrated by using data from a nuclear radiation release at tomsk and from a more complex simulated nuclear accident exercise

spatial analyticity of the solutions to the subcritical dissipative quasi geostrophic equations we employ a new bilinear estimate to show that solutions to the subcritical dissipative quasi geostrophic equations with initial data in the scaling invariant lebesgue space are analytic in space variables some decay in time estimates for space time derivatives are also obtained

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques

growth of solutions for qg and 2d euler equations the work of constantin majda tabak 1 developed an analogy between the quasi geostrophic and 3d euler equations constantin majda and tabak proposed a candidate for a singularity for the quasi geostrophic equation their numerics showed evidence of a blow up for a particular initial data where the level sets of the temperature contain a hyperbolic saddle the arms of the saddle tend to close in finite time producing a sharp front numerics studies done later by ohkitani yamada 8 and constantin nie schorghofer 2 with the same initial data suggested that instead of a singularity the derivatives of the temperature were increasing as double exponential in time the study of collapse on a curve was first studied in 1 for the quasi geostrophic equation where they considered a simplified ansatz for classical frontogenesis with trivial topology at the time of collapse the scalar is discontinuous across the curve x2 f x1 with different limiting values for the temperature on each side of the front they show that under this topology the directional field remains smooth up to the collapse which contradicts the following theorem proven in 1

a comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors predicting values of a spatially distributed variable such as the concentration of a mineral throughout an ore body or the level of contamination around a toxic waste dump can be accomplished by a regression procedure known as kriging kriging and other types of statistical inference for spatially distributed variables are based on models of stochastic processes y t t d called random field models a commonly used class of random field models are the intrinsic models for which the mean is constant and half of the variance of yt ys is a function called the semivariogram of the difference t s the type of kriging corresponding to an intrinsic model is called ordinary kriging the semivariogram which typically is taken to depend on one or more unknown parameters must be estimated prior to ordinary kriging various estimators of the semivariogram s parameters have been proposed for two gaussian intrinsic random field models we compare by a monte carlo simulation study the performance o