on the geometry of the term structure of interest rates we present recently developed geometric methods for the analysis of finite dimensional term structure models of the interest rates this includes an extension of the frobenius theorem for fr echet spaces in particular this approach puts new light on many of the classical models such as the hull white extended vasicek and cox ingersoll ross short rate models the notion of a finite dimensional realization fdr is central for this analysis we motivate it classify all generic fdrs and provide some new results for the corresponding factor processes such as hypoellipticity of its generators and the existence of smooth densities furthermore we include finite dimensional external factors thus admitting a stochastic volatility structure

existence of affine realizations for stochastic partial differential equations driven by levy processes the goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by levy processes admits an affine realization our results are accompanied by several examples arising in natural sciences and economics

on bruck loops of 2 power exponent the goal of this paper is two fold first we provide the information needed to study bol ar or bruck loops by applying group theoretic methods this information is used in this paper as well as in baumeister and stein 2010 bs3 and in stein 2009 s moreover we determine the groups associated to bruck loops of 2 power exponent under the assumption that every non abelian simple group s is either passive or isomorphic to psl2 q q 1 4 a 2 power in a separate paper it is proven that indeed every non abelian simple group s is either passive or isomorphic to psl2 q q 1 4 a 2 power stein 2009 s the results obtained here are used in baumeister and stein 2010 bs3 where we determine the structure of the groups associated to the finite bruck loops

bessel capacities on compact manifolds and their relation to poisson capacities a motivation for this paper comes from the role of choquet capacities in the study of semilinear elliptic partial differential equations in particular the recent progress in the classification of all positive solutions of lu u in a bounded smooth domain e rd was achieved by using as a tool capacities on a smooth manifold e either the poisson capacities associated with the poisson kernel in e or the bessel capacities related to the bessel kernel have been used in this and many other applications there is no advantage in choosing any special member in a class of equivalent capacities two capacities are called equivalent if their ratio is bounded away from 0 and in the literature bessel capacities are considered mostly in the space rd we introduce two versions of bessel capacities on a compact n dimensional manifold a class capl p of equivalent capacities is defined for lp n on every compact lipschitz manifold another class cbl p is defined for all l 0 p 1 in terms of a diffusion process on a c2 manifold these classes coincide when both are defined if the manifold is the boundary of a bounded c2 domain e rd then both versions of the bessel capacities are equivalent to the poisson capacities

finite bruck loops bruck loops are bol loops satisfying the automorphic inverse property we prove a structure theorem for finite bruck loops x showing that x is essentially the direct product of a bruck loop of odd order with a 2 element bruck loop the former class of loops is well understood we identify the minimal obstructions to the conjecture that all finite 2 element bruck loops are 2 loops leaving open the question of whether such obstructions actually exist

an alternative approach on the existence of affine realizations for hjm term structure models we propose an alternative approach on the existence of affine realizations for heath jarrow and morton interest rate models it is applicable to a wide class of models and simultaneously it is conceptually rather comprehensible we also supplement some known existence results for particular volatility structures and provide further insights into the geometry of term structure models

invariance of closed convex cones for stochastic partial differential equations abstract the goal of this paper is to clarify when a closed convex cone is invariant for a stochastic partial differential equation spde driven by a wiener process and a poisson random measure and to provide conditions on the parameters of the spde which are necessary and sufficient

a class of boundary traces for solutions of the equation lu ψ u our subject is the class u of all positive solutions of a semilinear equation lu u in e where l is a second order elliptic differential operator e is a domain in rd and belongs to a convex class of c1 functions which contains functions u u with 1 a special role is played by a class u0 of solutions which we call moderate a solution u is moderate if there exists h u such that lh 0 in e we say that u u is moderate if u is the limit of an increasing sequence of moderate solutions in e b dynkin s e kuznetsov fine topology and fine trace on the boundary associated with a class of quasilinear differential equations comm pure appl math 51 1998 897 936 all moderate solutions were classified by using their fine boundary traces 2 in m marcus l veron the precise boundary trace of positive solutions of the equation u uq in the supercritical case in perspectives in nonlinear partial differential equations in honor of haim brezis contemp math amer math soc providence ri 2007 arxiv org math 0610102 marcus and veron introduced a different characteristic called the precise trace for solutions of the equation u u with 1 in a bounded c2 domain in the present paper we develop a general scheme covering both approaches and we prove the equivalence in a certain sense of the fine and precise traces an implication of this equivalence is a wiener type criterion for vanishing of the poisson kernel of the equation lu x a x u x

the finite bruck loops abstract we continue the work of aschbacher kinyon and phillips 2006 akp06 as well as of glauberman 1964 1968 g64 g68 by describing the structure of the finite bruck loops we show that a finite bruck loop x is the direct product of a bruck loop of odd order with either a soluble bruck loop of 2 power order or a product of loops related to the groups psl 2 q q 9 or q 5 a fermat prime the latter possibility does occur as is shown in nagy 2008 n08 and baumeister and stein 2010 bs10 as corollaries we obtain versions of sylow s lagrange s and hall s theorems for loops

invariant manifolds for weak solutions to stochastic equations viability and invariance problems related to a stochastic equation in a hilbert space h are studied finite dimensional invariant c2 submanifolds of h are characterized we derive nagumo type conditions and prove a regularity result any weak solution which is viable in a finite dimensional c2 submanifold is a strong solution these results are related to finding finite dimensional realizations for stochastic equations there has recently been increased interest in connection with a model for the stochastic evolution of forward rate curves

bol loops and bruck loops of order pq abstract right bol loops are loops satisfying the identity z x y x z x y x and right bruck loops are right bol loops satisfying the identity x y 1 x 1 y 1 let p and q be odd primes such that p q advancing the research program of niederreiter and robinson from 1981 we classify right bol loops of order pq when q does not divide p 2 1 the only right bol loop of order pq is the cyclic group of order pq when q divides p 2 1 there are precisely p q 4 2 right bol loops of order pq up to isomorphism including a unique nonassociative right bruck loop b p q of order pq let q be a nonassociative right bol loop of order pq we prove that the right nucleus of q is trivial the left nucleus of q is normal and is equal to the unique subloop of order p in q and the right multiplication group of q has order p 2 q or p 3 q when q b p q the right multiplication group of q is isomorphic to the semidirect product of z p z p with z q finally we offer computational results as to the number of right bol loops of order pq up to isotopy

existence of invariant manifolds for stochastic equations in infinite dimension we provide a frobenius type existence result for finite dimensional invariant submanifolds for stochastic equations in infinite dimension in the spirit of da prato and zabczyk 5 we recapture and make use of the convenient calculus on frechet spaces as developed by kriegl and michor 16 our main result is a weak version of the frobenius theorem on frechet spaces as an application we characterize all finite dimensional realizations for a stochastic equation which describes the evolution of the term structure of interest rates

a class of finite simple bol loops of exponent 2 in this paper we give an infinite class of finite simple right bol loops of exponent 2 the right multiplication group of these loops is an extension of an elementary abelian 2 group by s 5 the construction uses the description of the structure of such loops given by m aschbacher 2005 these results answer some questions of m aschbacher

isolated involutions whose centraliser is soluble abstract we analyse a minimal counterexample to glauberman s z theorem from a local group theoretic point of view one of the main results is a group theoretic proof for the z theorem in the special case where the centraliser of an isolated involution is soluble

regularity of finite dimensional realizations for evolution equations we show that a continuous local semiflow of ck maps on a finite dimensional ck manifoldm can be embedded into a local ck flow on m under some weak necessary assumptions this result is applied to an open problem in 2 we prove that finite dimensional realizations for interest rate models are highly regular objects namely given by submanifolds m of d a where a is the generator of a strongly continuous semigroup