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

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

the quantum superalgebra uq osp 1 2n deformed para bose operators and root of unity representations we recall the relation between the lie superalgebra osp 1 2n and para bose operators the quantum superalgebra uq osp 1 2n defined as usual in terms of its chevalley generators is shown to be isomorphic to an associative algebra generated by so called pre oscillator operators satisfying a number of relations from these relations and the analogue with the non deformed case one can interpret these pre oscillator operators as deformed para bose operators some consequences for uq osp 1 2n cartan weyl basis poincare birkhoff win basis and its hopf subalgebra uq gl n are pointed out finally using a realization in terms of q commuting q bosons we construct an irreducible finite dimensional unitary fock representation of uq osp 1 2n and its decomposition in terms of uq gl n representations when q is a root of unity

statistical physics of the freely jointed chain using the method of constraints proposed by s f edwards and a g goodyear j phys a 5 965 1972 5 1188 1972 we do a complete calculation of the canonical partition function of a freely jointed chain fjc from its classical hamiltonian we show how the constraints reduce the phase space of an ideal gas of monomers to the phase space of a fjc and how they permit one to find the canonical partition function by using this function it is possible to study thermodynamical properties of fjc s and to build other thermodynamical ensembles via laplace transforms thus we define a grand canonical ensemble where the monomer number of the fjc can fluctuate in this ensemble the fjc of infinite length is the asymptotic state at low and high temperatures the critical exponents ensuremath gamma and ensuremath nu for fjc s are calculated and found to be equal to the gaussian polymer exponents connections between the properties of fjc s and random walks on regular lattices are also discussed textcopyright 1996 the american physical society

non linear rough heat equations this article is devoted to define and solve an evolution equation of the form dyt yt dt dx t yt wherestands for the laplace operator on a space of the form l p r n and x is a finite dimensional noisy nonlinearity whose typical form is given by xt n i 1 x i fi where each x x 1 x n is a holder function generating a rough path and each fi is a smooth enough function defined on l p r n the generalization of the usual rough path theory allowing to cope with such

quantum deformation of bose parastatistics a q deformation of the transformation of the chevalley basis to an odd basis of generators of the universal enveloping of the lie superalgebra g n osp 1 2n is presented it is shown that one thus obtains a reasonable quantum deformation of the algebra of n para bose oscillators

matrix representation of osp 2 2 in the u 1 1 basis vector coherent state theory is applied to matrix representations of osp 2 2 in the u 1 1 basis the branching rule of osp 2 2 1u 1 is derived finite dimensional irreducible matrix representations of osp 2 2 in the u 1 1 basis are discussed and matrix elements of osp 2 2 generators are obtained by using the k matrix technique

transformations of some induced osp 3 2 modules in an so 3 sp 2 basis the modules of the orthosymplectic lie superalgebra osp 3 2 induced from finite dimensional irreducible submodules of the stability subalgebra so 3 gl 1 are investigated the corresponding infinite dimensional irreducible or indecomposable modules the kac modules and the related typical and atypical modules are studied in detail every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so 3 sp 2 for each of these infinite dimensional or finite dimensional irreducible or indecomposable modules relations are written down giving the transformations of the basis under the action of the algebra generators

inertia tensor and size of a polymer chain guided by an approach used in the study of membranes we construct the partition function for a discrete gaussian chain model of polymers the hamiltonian is where describes the chain connectivity is the inertia tensor which gives the shape and size of the polymer chain and tr denotes the trace here we consider only the size which is obtained from the partition function by differentiating with respect to the conjugate variable the partition function is expressed in terms of the hypergeometric function an orthogonal polynomial where n is the number of monomers and is the ratio of and the coefficient in the limit corresponds to the random coil while the limit describes a compact object we also study the excluded volume problem by discretizing edwards continuous self avoidance term we obtain dimensionally regularized expressions for the radius of gyration and the end to end distance the short distance cut off dependence of the continuous model is reproduced

algebraic structure of green s ansatz and its q deformed analogue the algebraic structure of green s ansatz 1953 is analysed in such a way that its generalization to the case of q deformed para bose and para fermi operators becomes evident to this end the underlying lie super algebraic properties of the parastatistics are essentially used

backward doubly stochastic differential equations and systems of quasilinear spdes we introduce a new class of backward stochastic differential equations which allows us to produce a probabilistic representation of certain quasilinear stochastic partial differential equations thus extending the feynman kac formula for linear spde s

backward doubly stochastic volterra integral equations and their applications abstract in this paper we introduce a new class of equations called backward doubly stochastic volterra integral equations bdsvies for short first the well posedness of bdsvies in the sense of introduced m solutions is established second a comparison theorem of bdsvies is proved as an application of the comparison theorem we derive the existence of solutions of bdsvies with continuous coefficients third a duality principle between linear forward doubly stochastic volterra integral equations fdsvies for short and bdsvies is obtained moreover by virtue of the duality principle a maximum principle of pontryagin type is established for an optimal control problem of fdsvies

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

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

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

backward stochastic dynamics on a filtered probability space we demonstrate that backward stochastic differential equations bsde may be reformulated as ordinary functional differential equations on certain path spaces in this framework neither ito s integrals nor martingale representation formulate are needed this approach provides new tools for the study of bsde and is particularly useful for the study of bsde with partial information the approach allows us to study the following type of backward stochastic differential equations with y t on a general filtered probability space f f t p where b is a d dimensional brownian motion l is a prescribed nonlinear mapping which sends a square integrable m to an adapted process l m and m a correction term is a square integrable martingale to be determined under certain technical conditions we prove that the system admits a unique solution y m in general the associated partial differential equations are not only nonlinear but also may be nonlocal and involve integral operators

canonical partition functions of freely jointed chains the freely jointed chain is a simple off lattice ideal model of a heteropolymer we show how to compute the canonical partition function of this model exactly for all physical primary structures degree of polymerization and space dimensions greater than or equal to 2 the canonical partition function of this model of a heteropolymer has an analytical expression involving a complicated multiple hypergeometric function to obtain some accurate approximations we develop and use the independent motion approximation ima

wigner quantum oscillators we present three groups of non canonical quantum oscillators the position and momentum operators of each group generate basic lie superalgebras namely sl 1 3 osp 1 6 and osp 3 2 the sl 1 3 oscillators have finite energy spectrum and finite dimensions the osp 1 6 oscillators are related to the para bose statistics the internal angular momentum s of the osp 3 2 oscillators takes no more than three half integer values in a particular representation s 1 2

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

on the rough paths approach to non commutative stochastic calculus abstract we study different possibilities to apply the principles of rough paths theory in a non commutative probability setting first we extend previous results obtained by capitaine donati martin and victoir in lyons s original formulation of rough paths theory then we settle the bases of an alternative non commutative integration procedure in the spirit of gubinelli s controlled paths theory and which allows us to revisit the constructions of biane and speicher in the free brownian case new approximation results are also derived from the strategy

holonomic constraints an analytical result systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with hamiltonian or lagrangian dynamics the influence of holonomic constraints in equations of motions is taken into account by using lagrange multipliers finding the value of the lagrange multipliers allows us to compute the forces induced by the constraints and therefore to integrate the equations of motions of the system computing analytically the lagrange multipliers for a constrained system may be a difficult task that depends on the complexity of systems for complex systems it is most of the time impossible to achieve in computer simulations some algorithms using iterative procedures estimate numerically lagrange multipliers or constraint forces by correcting the unconstrained trajectory in this work we provide an analytical computation of the lagrange multipliers for a set of linear holonomic constraints with an arbitrary number of bonds of constant length in the appendix explicit formulae are shown for lagrange multipliers for systems having 1 2 3 4 and 5 bonds of constant length linearly connected

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

a non linear parabolic pde with a distributional coefficient and its applications to stochastic analysis abstract we consider a non linear parabolic partial differential equation pde on r d with a distributional coefficient in the non linear term the distribution is an element of a besov space with negative regularity and the non linearity is of quadratic type in the gradient of the unknown under suitable conditions on the parameters we prove local existence and uniqueness of a mild solution to the pde and investigate properties like continuity with respect to the initial condition and blow up times we prove a global existence and uniqueness result assuming further properties on the non linearity to conclude we consider an application of the pde to stochastic analysis in particular to a class of non linear backward stochastic differential equations with distributional drivers

rough evolution equations we generalize lyons rough paths theory in order to give a pathwise meaning to some nonlinear infinite dimensional evolution equation associated to an analytic semigroup and driven by an irregular noise as an illustration we discuss a class of linear and nonlinear 1d spdes driven by a space time gaussian noise with singular space covariance and brownian time dependence

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

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

freely jointed chains in external potentials analytical computations freely jointed chains in external potentials are crude representations of macromolecular systems in interaction with electrostatic fields surfaces walls and interfaces we show how the canonical partition function of these models can be computed analytically and how the independent motion approximation ima may be applied in particular the chain stretched at both ends is studied with ima and new results are obtained for entropic elastic constants and force extension relations including the dependence on the degree of polymerization these new results are in good agreement with molecular dynamics computations

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

partial differential equations driven by rough paths abstract we study a class of linear first and second order partial differential equations driven by weak geometric p rough paths and prove the existence of a unique solution for these equations this solution depends continuously on the driving rough path this allows a robust approach to stochastic partial differential equations in particular we may replace brownian motion by more general gaussian and markovian noise support theorems and large deviation statements all become easy corollaries of the corresponding statements of the driving process in the case of first order equations with gaussian noise we discuss the existence of a density with respect to the lebesgue measure for the solution

backward stochastic differential equations with rough drivers backward stochastic differential equations bsdes in the sense of pardoux peng lecture notes in control and inform sci 176 1992 200 217 provide a non markovian extension to certain classes of nonlinear partial differential equations the nonlinearity is expressed in the so called driver of the bsde our aim is to deal with drivers which have very little regularity in time to this end we establish continuity of bsde solutions with respect to rough path metrics in the sense of lyons rev mat iberoam 14 1998 215 310 and so obtain a notion of bsde with rough driver existence uniqueness and a version of lyons limit theorem in this context are established our main tool aside from rough path analysis is the stability theory for quadratic bsdes due to kobylanski ann probab 28 2000 558 602

on a modelled rough heat equation we use the formalism of hairer s regularity structures theory to study a heat equation model with non linear perturbation driven by a space time fractional noise different regimes are observed depending on the global pathwise roughness of the noise to this end and following the procedure exhibited in hairer invent math 198 2 269 504 2014 the equation is first lifted into some abstract regularity structure and therein solved through a fixed point argument then we construct a consistent model above the fractional noise by relying on a smooth fourier type approximation of the process

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

backward doubly stochastic differential equations with random coefficients and quasilinear stochastic pdes abstract in this paper by virtue of malliavin calculus we establish a relationship between backward doubly stochastic differential equations with random coefficients and quasilinear stochastic pdes and thus extend the well known nonlinear stochastic feynman kac formula of pardoux and peng 13 to non markovian case

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

a priori estimates for rough pdes with application to rough conservation laws we introduce a general framework to study pdes driven by rough paths we develop new a priori estimates based on a rough gronwall lemma argument for weak solutions to rough pdes this will allow us to follow standard pde strategies to obtain existence and uniqueness results in particular our approach does not rely on any sort of transformation formula flow transformation feynman kac representation formula etc and is therefore rather flexible as an application we study conservation laws driven by rough paths establishing well posedness for the corresponding kinetic formulation

a description of the superalgebra osp 2 n 1 2 m via green generators an alternative description of the lie superalgebra osp 2n 1 2m in terms of generators and relations is given the generators called green generators are the root vectors of osp 2n 1 2m corresponding to the orthogonal roots

probabilistic interpretation for solutions of fully nonlinear stochastic pdes in this article we propose a wellposedness theory for a class of second order backward doubly stochastic differential equation 2bdsde we prove existence and uniqueness of the solution under a lipschitz type assumption on the generator and we investigate the links between the 2bdsdes and a class of parabolic fully nonlinear stochastic pdes precisely we show that the markovian solution of 2bdsdes provide a probabilistic interpretation of the classical and stochastic viscosity solution of fully nonlinear spdes

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

rough path stability of semi linear spdes we give meaning to linear and semi linear possibly degenerate parabolic partial differential equations with affine linear rough path noise and establish stability in a rough path metric in the case of enhanced brownian motion brownian motion with its levy area as rough path noise the solution coincides with the standard variational solution of the spde

hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the jordan schwinger map the aim of this paper is to show that there is a hopf structure of the parabosonic and parafermionic algebras and this hopf structure can generate the well known hopf algebraic structure of the lie algebras through a realization of lie algebras using the parabosonic and parafermionic extension of the jordan schwinger map the differences between the hopf algebraic and the graded hopf superalgebraic structure on the parabosonic algebra are discussed

finite and infinite dimensional representations of the orthosymplectic superalgebra osp 3 2 the shift operator technique is used to give a complete analysis of all finite and infinite dimensional irreducible representations of the orthosymplectic superalgebra osp 3 2 for all cases the star or grade star conditions for the algebra are investigated only two finite dimensional representations are grade star representations if the representation space is required to be a graded hilbert space when the even part is so 3 sp 2 r su 2 su 1 1 an infinite class of infinite dimensional star representations is found one of them can be realized in terms of two valued functions of a complex variable this representation reduces to the sum of two metaplectic representations of sp 2 we show that it is precisely this metaplectic representation for osp 3 2 which gives the spin energy eigenstates for the one dimensional harmonic oscillator with spin 1 2 states