centers of reduced enveloping algebras we compute the inverse image of a functional in the zassenhaus variety we apply this computation to describe the category of representations for a regular functional

the center of the enveloping algebra of the p lie algebras n n n when p divides n abstract let be a reductive lie algebra over an algebraically closed field f with char f p 0 suppose g satisfies jantzen s standard assumptions then the structure of z the center of the enveloping algebra is described by the extended veldkamp s theorem we examine here the deviation of z from this theorem in case or and p n it is shown that veldkamp s description is valid for this implies that friedlander parshall donkin decomposition theorem for holds in case p is good for a semi simple simply connected g excluding if p 2 a 1 factors of g in case or we prove a fiber product theorem for a polynomial extension of z however veldkamp s description mostly fails for and in particular z is not cohen macaulay if n 4 in both cases contrary to a result of kac weisfeiler we show for an odd prime p that and do not generate we also show for that the codimension of the non azumaya locus of z is at least 2 if n 3 and exceeds 2 if n 4 this refutes a conjecture of brown goodearl we then show that z is factorial excluding thus confirming a conjecture of premet tange we also verify humphreys conjecture on the parametrization of blocks in case p is good for g

unbiased estimation with square root convergence for sde models in many settings in which monte carlo methods are applied there may be no known algorithm for exactly generating the random object for which an expectation is to be computed frequently however one can generate arbitrarily close approximations to the random object we introduce a simple randomization idea for creating unbiased estimators in such a setting based on a sequence of approximations applying this idea to computing expectations of path functionals associated with stochastic differential equations sdes we construct finite variance unbiased estimators with a square root convergence rate for a general class of multidimensional sdes we then identify the optimal randomization distribution numerical experiments with various path functionals of continuous time processes that often arise in finance illustrate the effectiveness of our new approach

sinc galerkin method for solving biharmonic problems there are many techniques available to numerically solve the biharmonic equation in this paper we show that the sinc galerkin method is a very effective tool in numerically solving this equation hermite interpolation is used to treat the nonhomogeneous boundary conditions our method is tested on examples and comparisons with other methods are made it is shown that the sinc galerkin method yields good results even when singularities occur at the boundaries

an indirect boundary integral equation method for the biharmonic equation an integral equation method for the dirichlet problem for the biharmonic equation is proposed it leads to a 2 times 2 matrix integral equation system by taking suitable norms on the spaces of density functions the fredholm operator theory can be used to prove the solvability the kernels in this system are relatively complicated therefore especially when a high order polynomial approximation is used for a numerical purpose it is costly to evaluate the integrals that appear in the numerical system a discrete galerkin method that has shown superb convergence is proposed here as in k atkinson j integral equations appl 1 1988 pp 343 363 and elsewhere when the boundary functions are smooth exponential convergence is observed

some discrete methods for boundary integral equations on smooth closed curves in this paper discrete trigonometric methods as well as quadrature methods for solution of boundary integral equations on smooth closed curves are presented and analyzed the analysis applies the general approach based on the consistency stability and convergence properties the trigonometric methods including e g variants based on product integration turn out to have high convergence even exponential convergence the family of quadrature methods covers operators with the even symbol and of order beta 0 they can be considered as fully discretized petrov galerkin methods that employ approximations both for the integral operator and the inner product the operator is approximated by using the trapezoidal rule either directly or after subtraction of the kernel singularity for instance for symm s equation beta 1 a method with the rate o h 5 of convergence is presented furthermore the quadrature solution of the cauchy singular integral equation beta 0 and the hypersingular

trigonometric collocation methods with product integration for boundary integral equations on closed curves considering boundary integral equations on smooth closed curves the product integration methods have turned out to be very efficient to define fully discrete schemes with a high convergence rate here we give a general approach to product integration methods in connection with the trigonometric collocation the discretization scheme has arbitrarily high convergence rate even exponential if the solution and the curve are analytic applications and numerical experiments confirming our theoretical results are discussed

random generation of stochastic area integrals the authors describe a method of random generation of the integrals a 1 2 t t h int t t h int t s dw 1 r dw 2 s int t t h int t s dw 2 r dw 1 s together with the increments w 1 t h w 1 t and w 2 t h w 2 t of a two dimensional brownian path w 1 t w 2 t the method chosen is based on marsaglia s rectangle wedge tail method generalised to higher dimensions the motivation is the need for a numerical scheme for simulation of strong solutions of general multidimensional stochastic differential equations with an order of convergence o h where h is the stepsize previously no method has obtained an order of convergence better than o sqrt h in the general case

new indirect scalar boundary integral equation formulas for the biharmonic equation we derive scalar boundary integral equation formulas for both interior and exterior biharmonic equations with the dirichlet boundary data they are based on indirect boundary integral equation formulas so called the chakrabarty and almansi formulas the scalar formulas are derived through an unconventional variational approach the unique solvability results of the formulas are also obtained

local error estimates for some petrov galerkin methods applied to strongly elliptic equations on curves on etudie les proprietes de convergence locales de quelques methodes de petrov galerkin appliquees aux equations fortement elliptiques sur des courbes regulieres du plan on etablit des estimations d erreurs locales pour une grande echelle de normes de sobolev

an adaptive timestepping algorithm for stochastic differential equations we introduce a variable timestepping procedure using local error control for the pathwise strong numerical integration of a system of stochastic differential equations forced by a single wiener process the milstein method is used to advance the numerical solution and the stepsizes are determined via two local error estimates that roughly correspond to leading order deterministic and stochastic local error components one advantage of using two error controls is an increased flexibility that allows for the treatment of both drift and diffusion dominated regimes in a consistent manner numerical results are presented and the generalization of this approach to wider classes of problems and methods is discussed

multilevel monte carlo path simulation we show that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using monte carlo path simulations in the simplest case of a lipschitz payoff and a euler discretisation the computational cost to achieve an accuracy of o e is reduced from o e 3 to o e 2 log e 2 the analysis is supported by numerical results showing significant computational savings

numerical analysis of stochastic schemes in geophysics we present and study the stability convergence and order of convergence of a numerical scheme used in geophysics namely the stochastic version of a deterministic implicit leapfrog scheme which has been developed for the approximation of the so called barotropic vorticity model two other schemes which might be useful in the context of geophysical applications are also introduced and discussed

factorial properties of the enveloping algebra of a nilpotent lie algebra in prime characteristic abstract let u l be the enveloping algebra of a finite dimensional nilpotent lie algebra l over a prime characteristic field we prove that its center z u l is a unique factorization ufd we also show that u l has a non commutative ufd property namely each height one prime ideal in u l is generated by a central element we prove both results simultaneously using non commutative pi maximal order technique our results are prime characteristic analogues of similar ones in characteristic zero which are due to dixmier j dixmier sur l algebre enveloppante d une algebra de lie nilpotente arch math 10 1959 321 32 and moeglin c moeglin factorialite dans les algebres enveloppantes c r acad sci paris a 282 1976 1269 1272 we have recently applied these results to show that u l is a calabi yau algebra

on the center and semi center of enveloping algebras in prime characteristic abstract theorems of j dixmier and c moeglin on the semi center of enveloping algebras in zero characteristic and of r p stanley and h nakajima on polynomial relative invariants of finite groups are shown to have analogs for enveloping algebras and for lie algebra polynomial invariants in the prime characteristic case we shall illustrate by examples the extent of these analogies a key result is the realization of the semi center as a fixed ring of the action of a finite set of nilpotent derivations on the center of an enveloping algebra of a related lie algebra

the ramification of centres lie algebras in positive characteristic and quantised enveloping algebras let h be a hopf algebra over the field k which is a finite module over a central affine sub hopf algebra r examples include enveloping algebras u mathfrak g of finite dimensional k lie algebras mathfrak g in positive characteristic and quantised enveloping algebras and quantised function algebras at roots of unity the ramification behaviour of the maximal ideals of z h with respect to the subalgebra r is studied and the conclusions are then applied to the cases of classical and quantised enveloping algebras in the case of u mathfrak g for mathfrak g semisimple a conjecture of humphreys 28 on the block structure of u mathfrak g is confirmed in the case of u epsilon mathfrak g for mathfrak g semisimple and epsilon an odd root of unity we obtain a quantum analogue of a result of mirkovic and rumynin 35 and we fully describe the factor algebras lying over the regular sheet 9 the blocks of u epsilon mathfrak g are determined and a necessary condition which may also be sufficient for a baby verma u epsilon mathfrak g module to be simple is obtained

factoriality for the reductive zassenhaus variety and quantum enveloping algebra let u g be the enveloping algebra of a finite dimensional reductive lie algebra g over an algebraically closed field of prime characteristic let u p s be the simply connected quantum enveloping algebra at the root of unity of a complex semi simple finite dimensional lie algebra s we show by similar proofs that the centers of both are factorial while the first result was established by r tange 32 by different methods the second one confirms a conjecture in 4 we also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic

variable step size control in the numerical solution of stochastic differential equations we introduce a variable step size method for the numerical approximation of pathwise solutions to stochastic differential equations sdes the method which is dependent on a representation of bro

the centre of quantum sln at a root of unity abstract it is proved that the centre z of the simply connected quantised universal enveloping algebra over c u e p sl n e a primitive l th root of unity l an odd integer 1 has a rational field of fractions furthermore it is proved that if l is a power of an odd prime z is a unique factorisation domain

approximation of multiple stochastic integrals and its application to stochastic differential equations abstract as multiple stochastic integrals are not very easy to simulate we would like to treat them as solutions of systems of stochastic differential equations and solve them successively and recursively approximated by the stochastic taylor expansion as a chen series in terms of a philip hall basis or lyndon basis we can save sufficient values of multiple stochastic integrals with independent sample paths in a look up table for future use the table can be used to implement high order schemes to solve stochastic differential equations numerically a numerical example will be shown to illustrate the efficiency

factorisation properties of group scheme actions let h be an algebraic group scheme over a field k acting on a commutative k algebra a which is a unique factorisation domain we show that under certain mild assumptions the monoid of nonzero h stable principal ideals in a is free commutative from this we deduce in certain special cases results about the monoid of nonzero semi invariants and the algebra of invariants we use an infinitesimal method which allows us to work over an arbitrary base field

discrete time approximations of stochastic delay equations the milstein scheme in this paper we develop a strong milstein approximation scheme for solving stochastic delay differential equations sddes the scheme has convergence order 1 in order to establish the scheme we prove an infinite dimensional ito formula for tame functions acting on the segment process of the solution of an sdde it is interesting to note that the presence of the memory in the sdde requires the use of the malliavin calculus and the anticipating stochastic analysis of nualart and pardoux given the nonanticipating nature of the sdde the use of anticipating calculus methods in the context of strong approximation schemes appears to be novel

new boundary element formulas for plane elasticity abstract a plane elasticity problem leads us to a biharmonic equation with the boundary condition consisting of first order partial derivatives we apply the boundary integral equation formulas by y jeon 1996 for the problem derivation of the formulas and the concerned analysis and numerical examples are presented the formulas are especially efficient in evaluating the stress tensor on the boundary as well as inside the domain it is the stress tensor components that are physically important quantities for the problem

a method for solving an inverse biharmonic problem this paper deals with the problem of determining of an unknown coefficient in an inverse boundary value problem using a nonconstant overspecified data it has been shown that the solution to this inverse problem exists and is unique

a new boundary integral formulation for stream function and vorticity in axisymmetric stokes flow a boundary integral equation approach is presented to solve the flow stream function and vorticity in the axisymmetric stokes problem without swirl the governing equations expressed in these variables require that the fundamental solutions of the involved differential operators be found the fundamental solutions in a closed form suitable for numerical treatment of integral equations are obtained and their equivalent forms in infinite integral are derived by using fourier and hankel transforms a coupled system of boundary integral equations for the stream function and the vorticity is formulated by employing new fundamental solutions solution of these equations is realized by the collocation method numerical results are included for several bounded and unbounded domain problems to validate and demonstrate the effectiveness of the proposed approach

on the asymptotic convergence of collocation methods we prove quasioptimal and optimal order estimates in various sobolev norms for the approximation of linear strongly elliptic pseudodifferential equations in one independent variable by the method of nodal collocation by odd degree polynomial splines the analysis pertains in particular to many of the boundary element methods used for numerical computation in engineering applications equations to which the analysis is applied include fredholm integral equations of the second kind certain first kind fredholm equations singular integral equations involving cauchy kernels a variety of integro differential equations and two point boundary value problems for ordinary differential equations the error analysis is based on an equivalence which we establish between the collocation methods and certain nonstandard galerkin methods we compare the collocation method with a standard galerkin method using splines of the same degree showing that the galerkin method is quasioptimal in a sobolev space of lower index and furnishes optimal order approximation for a range of sobolev indices containing and extending below that for the collocation method and so the standard galerkin method achieves higher rates of convergence

modular lie algebras and the gelfand kirillov conjecture let mathfrak g be a finite dimensional simple lie algebra over an algebraically closed field mathbb k of characteristic 0 let mathfrak g mathbb z be a chevalley form of mathfrak g and mathfrak g bbbk mathfrak g mathbb z otimes mathbb z bbbk where bbbk is the algebraic closure of mathbb f p let g bbbk be a simple simply connected algebraic bbbk group with operatorname lie g bbbk mathfrak g bbbk in this paper we apply recent results of rudolf tange on the fraction field of the centre of the universal enveloping algebra u mathfrak g bbbk to show that if the gelfand kirillov conjecture from 1966 holds for mathfrak g then for all p 0 the field of rational functions bbbk mathfrak g bbbk is purely transcendental over its subfield bbbk mathfrak g bbbk g bbbk very recently it was proved by colliot thelene kunyavski popov and reichstein that the field of rational functions mathbb k mathfrak g is not purely transcendental over its subfield mathbb k mathfrak g mathfrak g if mathfrak g is of type b n n 3 d n n 4 e6 e7 e8 or f4 we prove a modular version of this result valid for p 0 and use it to show that in characteristic 0 the gelfand kirillov conjecture fails for the simple lie algebras of the above types in other words if mathfrak g is of type b n n 3 d n n 4 e6 e7 e8 or f4 then the lie field of mathfrak g is more complicated than expected

on the asymptotic convergence of collocation methods with spline functions of even degree we investigate the collocation of linear one dimensional strongly elliptic integro dif ferential or more generally pseudo differential equations on closed curves by even degree polynomial splines the equations are collocated at the respective midpoints subject to uniform nodal grids of the even degree s splines we prove quasioptimal and optimal order asymptotic error estimates in a scale of sobolev spaces the results apply in particular to boundary element methods used for numerical computations in engineering applications the equations considered include fredholm integral equations of the second and the first kind singular integral equations involving cauchy kernels and integro differential equations having convolutional or constant coefficient principal parts respectively the error analysis is based on an equivalence between the collocation and certain varia tional methods with different degree splines as trial and as test functions we further need to restrict our operators essentially to pseudo differential operators having convolutional prin cipal part this allows an explicit fourier analysis of our operators as well as of the spline spaces in terms of trigonometric polynomials providing babuska s stability condition based on strong ellipticity our asymptotic error estimates extend partly those obtained by d n arnold and w l wendland from the case of odd degree splines to the case of even degree splines 1 introduction in this paper we investigate the asymptotic convergence of the collocation method using even degree polynomial splines applied to strongly elliptic systems of pseudo differential equations on closed curves with convolutional prin cipal part the collocation here employs the gauss points of one point integration as collocation points which corresponds to the usual boundary element collocation in applications 5 12 17 19 26 31 34 this is in contrast to the method investigated by g schmidt in 29 where one collocates at the break points of even order splines the asymptotic convergence properties for the standard galerkin method with splines of arbitrary orders are well known 22 for the collocation method however asymptotic convergence up to now has been shown for strongly elliptic systems only in the case of odd order splines by d n arnold and w l wendland 7

the zassenhaus variety of a reductive lie algebra in positive characteristic let g be the lie algebra of a connected reductive group g over an algebraically closed field k of characteristic p 0 let z be the centre of the universal enveloping algebra u u g of g its maximal spectrum is called the zassenhaus variety of g we show that under certain mild assumptions on g the field of fractions frac z of z is g equivariantly isomorphic to the function field of the dual space g with twisted g action in particular frac z is rational this confirms a conjecture of j alev furthermore we show that z is a unique factorisation domain confirming a conjecture of a braun and c hajarnavis recently a premet used the above result about frac z a result of colliot thelene kunyavskii popov and reichstein and reduction mod p arguments to show that the gelfand kirillov conjecture cannot hold for simple complex lie algebras that are not of type a c or g2

product expansion for stochastic jump diffusions and its application to numerical approximation abstract we derive a product expansion of the exponential lie series in terms of a philip hall basis for the chen series corresponding to the stochastic jump diffusion as in sussmann in c i byrnes and a lindquist eds theory and applications of nonlinear control systems north holland amsterdam 1986 pp 323 335 for the deterministic case based on the expansion we establish the stratonovich taylor hall sth schemes such that each scheme involves only the minimum number of multiple stochastic integrals which can be regarded as systems of stochastic differential equations and approximated by a lower order scheme with an appropriate step size to ensure the necessary accuracy mean square convergence of the sth schemes is shown and numerical examples are provided to illustrate the results

homological aspects of noetherian pi hopf algebras and irreducible modules of maximal dimension abstract we prove that a noetherian hopf algebra of finite global dimension possesses further attractive homological properties at least when it satisfies a polynomial identity this applies in particular to quantized enveloping algebras and to quantized function algebras at a root of unity as well as to classical enveloping algebras in positive characteristic in all three cases we show that these algebras are auslander regular and macaulay we derive representation theoretic consequences concerning the coincidence of the non azumaya and singular loci for each of the above three classes of algebras

block representation type of reduced enveloping algebras let k be an algebraically closed field of characteristic p g a connected reductive k group g lie g x e g and u x g the reduced enveloping algebra of g associated with x assume that g 1 is simply connected p is good for g and g has a non degenerate g invariant bilinear form all blocks of u x g having finite and tame representation type are determined

quadrature methods for strongly elliptic equations of negative order on smooth closed curves in this article the authors introduce and analyze a family of simple quadrature methods for strongly elliptic equations of negative order the results cover all the classical pseudodifferential equations of this kind and hence the boundary integral equations appearing in applications the quadrature methods are based on the trapezoidal approximation of the operator with respect to a uniform mesh and on varepsilon collocation they are proved to have the stability and the convergence with the maximal rate o h beta of convergence in general and o h beta 1 for some special values of varepsilon here beta is the order of the operator the method is applicable to systems of boundary integral equations as well in this connection the authors have conducted some numerical experiments which confirm their theoretical results

duality estimates for the numerical solution of integral equations we formulate and prove aubin nitsche type duality estimates for the error of general projection methods examples of applications include collocation methods and augmented galerkin methods for boundary integral equations on plane domains with corners and three dimensional screen and crack problems for some of these methods we obtain higher order error estimates in negative norms in cases where previous formulations of the duality arguments were not applicable

a spline trigonometric galerkin method and an exponentially convergent boundary integral method we consider a galerkin method for functional equations in one space variable which uses periodic cardinal splines as trial functions and trigonometric polynomials as test functions we analyze the method applied to the integral equation of the first kind arising from a single layer potential formulation of the dirichlet problem in the interior or exterior of an analytic plane curve in constrast to ordinary spline galerkin methods we show that the method is stable and so provides quasioptimal approximation in a large family of hilbert spaces including all the sobolev spaces of negative order as a consequence we prove that the approximate solution to the dirichlet problem and all its derivatives converge pointwise with exponential rate

convergence of numerical schemes for the solution of parabolic stochastic partial differential equations we consider the numerical solution of the stochastic partial differential equation u t 2 u x 2 u w x t where w is space time white noise using finite differences for this equation gyongy has obtained an estimate of the rate of convergence for a simple scheme based on integrals of w over a rectangular grid we investigate the extent to which this order of convergence can be improved and find that better approximations are possible for the case of additive noise u 1 if we wish to estimate space averages of the solution rather than pointwise estimates or if we are permitted to generate other functionals of the noise but for multiplicative noise u u we show that no such improvements are possible

two dimensional multiple non homogeneous harmonic equation and its boundary integral equations the paper discusses 2 dimensional multiple non homogeneous harmonic equation and its boundary integral equation and gives recurrence formulae of fundamental solution under the assumption that non homogeneous term is m degree harmonic the integral term in domain is shifted into boundary integral therefore the boundary integral equations are obtained that the integral in domain is not included and the special solution can be expressed by boundary integrals furthermore the error and convergence analysis are given by taylor s polynomial approximating non homogeneous term f x and analytic expressions of boundary integral for 2 dimensional harmonic equation are given in local right angle coordinate system

higher order time integration of coulomb collisions in a plasma using langevin equations the extension of langevin equation monte carlo algorithms for coulomb collisions from the conventional euler maruyama time integration to the next higher order of accuracy the milstein scheme has been developed implemented and tested this extension proceeds via a formulation of the angular scattering directly as stochastic differential equations in the fixed frame spherical coordinate velocity variables results from the numerical implementation show the expected improvement o dt vs o dt 1 2 in the strong convergence rate both for the speed v and angular components of the scattering an important result is that this improved convergence is achieved for the angular component of the scattering if and only if the area integral terms in the milstein scheme are included the resulting milstein scheme is of value as a step towards algorithms with both improved accuracy and efficiency these include both algorithms with improved convergence in the averages weak convergence and multi time level schemes the latter have been shown to give a greatly reduced cost for a given overall error level when compared with conventional monte carlo schemes and their performance is improved considerably when the milstein algorithm is used for the underlying time advance versus the euler maruyama algorithm a new method for sampling the area integrals is given which is a simplification of an earlier direct method and which retains high accuracy this method while being useful in its own right because of its relative simplicity is also expected to considerably reduce the computational requirements for the direct conditional sampling of the area integrals that is needed for adaptive strong integration

some boundary element methods using dirac s distributions as trial functions in this article a boundary element method using dirac s distributions as trial functions is proposed as test functions we use smoother splines the computational complexity of this method is comparable with the collocation method and it converges with less regularity requirements on the boundary data asymptotic error analysis is derived an example considering solution of the potential problem is discussed in some detail finally a numerical example demonstrates the applicability of the method in practical calculations

zassenhaus varieties of general linear lie algebras abstract let g be a lie algebra over an algebraically closed field of characteristic p 0 and let u g be the universal enveloping algebra of g we prove in this paper for g gl n and g sl n that the centre of u g is a unique factorisation domain and its field of fractions is rational for g sl n our argument requires the assumption that p n while for g gl n it works for any p it turned out that our two main results are closely related to each other the first one confirms in type a a recent conjecture of a braun and c hajarnavis while the second answers a question of j alev

on symmetric smooth and calabi yau algebras one possible definition for a calabi yau algebra is a symmetric smooth pi algebra our main purpose here is to prove some necessary and sufficient criteria for verifying the local symmetric property in smooth pi algebras many known smooth pi algebras are shown to have this property in particular quantum enveloping algebras of complex semi simple lie algebras in the root of unity case and the enveloping algebra of sl n with p n 1 in characteristic p are typical examples a surprising result is that the inj dimt is finite where t is the trace ring of m n n generic matrices over a field of zero characteristic

efficient strong integrators for linear stochastic systems we present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of wiener processes these schemes are based on the neumann stochastic taylor and magnus expansions first we consider the case when the governing linear diffusion vector fields commute with each other but not with the linear drift vector field we prove that numerical methods based on the magnus expansion are more accurate in the mean square sense than corresponding stochastic taylor integration schemes second we derive the maximal rate of convergence for arbitrary multidimensional stochastic integrals approximated by their conditional expectations consequently for general nonlinear stochastic differential equations with noncommuting vector fields we deduce explicit formulae for the relation between error and computational costs for methods of arbitrary order third we consider the consequences in two numerical studies one of which is an application arising in stochastic linear quadratic optimal control

runge kutta methods for the strong approximation of solutions of stochastic differential equations some new stochastic runge kutta srk methods for the strong approximation of solutions of stochastic differential equations sdes with improved efficiency are introduced their convergence is proved by applying multicolored rooted tree analysis order conditions for the coefficients of explicit and implicit srk methods are calculated as the main novelty order 1 0 strong srk methods with significantly reduced computational complexity for ito as well as for stratonovich sdes with a multidimensional driving wiener process are presented where the number of stages is independent of the dimension of the wiener process further an order 1 0 strong srk method customized for ito sdes with commutative noise is introduced finally some order 1 5 strong srk methods for sdes with scalar diagonal and additive noise are proposed all introduced srk methods feature significantly reduced computational complexity compared to well known schemes

modular representation theory of lie algebras on etudie les representations non necessairement restreintes de l algebre universelle enveloppante u 7b g pour une algebre de lie restreinte 7b g

sdelab a package for solving stochastic differential equations in matlab we introduce sdelab a package for solving stochastic differential equations sdes within matlab sdelab features explicit and implicit integrators for a general class of ito and stratonovich sdes including milstein s method sophisticated algorithms for iterated stochastic integrals and flexible plotting facilities