spatio temporal covariance and cross covariance functions of the great circle distance on a sphere abstractin this article we propose stationary covariance functions for processes that evolve temporally over a sphere as well as cross covariance functions for multivariate random fields defined over a sphere for such processes the great circle distance is the natural metric that should be used to describe spatial dependence given the mathematical difficulties for the construction of covariance functions for processes defined over spheres cross time approximations of the state of nature have been proposed in the literature by using the euclidean based on map projections and the chordal distances we present several methods of construction based on the great circle distance and provide closed form expressions for both spatio temporal and multivariate cases a simulation study assesses the discrepancy between the great circle distance chordal distance and euclidean distance based on a map projection both in terms of estimation and prediction in a space time and a bivariate spatial setting where t

prefix free regular languages and pattern matching we explore the regular expression matching problem with respect to prefix freeness of the pattern we prove that a prefix free regular expression gives only a linear number of matching substrings in the size of a given text based on this observation we propose an efficient algorithm for the prefix free regular expression matching problem furthermore we suggest an algorithm to determine whether or not a given regular language is prefix free

exact simulation of stochastic volatility and other affine jump diffusion processes the stochastic differential equations for affine jump diffusion models do not yield exact solutions that can be directly simulated discretization methods can be used for simulating security prices under these models however discretization introduces bias into the simulation results and a large number of time steps may be needed to reduce the discretization bias to an acceptable level this paper suggests a method for the exact simulation of the stock price and variance under hestons stochastic volatility model and other affine jump diffusion processes the sample stock price and variance from the exact distribution can then be used to generate an unbiased estimator of the price of a derivative security we compare our method with the more conventional euler discretization method and demonstrate the faster convergence rate of the error in our method specifically our method achieves an o s 1 2 convergence rate where s is the total computational budget the convergence rate for the euler discretization method is o s 1 3 or slower depending on the model coefficients and option payoff function

asymptotic laws of planar brownian motion on presente des resultats recents sur la distribution asymptotique des nombres de passages et d enroulements

brownian charges around loops let x t n be a poisson sequence of independent brownian motions in d d 3 let be a compact oriented submanifold of d of dimensiond 2 and volume l let t be the sum of the windings of x s n 0 s t around then t t converges in law towards a cauchy variable of parameter l 2 a similar result is valid when the winding is replaced by the integral of a harmonic 1 form in d

matern cross covariance functions for multivariate random fields we introduce a flexible parametric family of matrix valued covariance functions for multivariate spatial random fields where each constituent component is a matern process the model parameters are interpretable in terms of process variance smoothness correlation length and colocated correlation coefficients which can be positive or negative both the marginal and the cross covariance functions are of the matern type in a data example on error fields for numerical predictions of surface pressure and temperature over the north american pacific northwest we compare the bivariate matern model to the traditional linear model of coregionalization

some extensions of the arc sine law as partial consequences of the scaling property of brownian motion the scaling property of brownian motion is exploited systematically in order to extend paul levy s arc sine law to brownian motion perturbed by its local time at 0 other important ingredients of the proofs are some ray knight theorems for local times

wright fisher diffusion with negative mutation rates we study a family of n dimensional diffusions taking values in the unit simplex of vectors with nonnegative coordinates that add up to one these processes satisfy stochastic differential equations which are similar to the ones for the classical wright fisher diffusions except that the mutation rates are now nonpositive this model suggested by aldous appears in the study of a conjectured diffusion limit for a markov chain on cladograms the striking feature of these models is that the boundary is not reflecting and we kill the process once it hits the boundary we derive the explicit exit distribution from the simplex and probabilistic bounds on the exit time we also prove that these processes can be viewed as a stochastic time reversal of a wright fisher process of increasing dimensions and conditioned at a random time a key idea in our proofs is a skew product construction using certain one dimensional diffusions called bessel square processes of negative dimensions which have been recently introduced by going jaeschke and yor

generalized arcsine laws for fractional brownian motion the three arcsine laws for brownian motion are a cornerstone of extreme value statistics for a brownian b t starting from the origin and evolving during time t one considers the following three observables i the duration t the process is positive ii the time t mathrm last the process last visits the origin and iii the time t mathrm max when it achieves its maximum or minimum all three observables have the same cumulative probability distribution expressed as an arcsine function thus the name arcsine laws we show how these laws change for fractional brownian motion x t a non markovian gaussian process indexed by the hurst exponent h it generalizes standard brownian motion i e h frac 1 2 we obtain the three probabilities using a perturbative expansion in h ensuremath frac 1 2 while all three probabilities are different this distinction can only be made at second order in our results are confirmed to high precision by extensive numerical simulations

the size of higman haines sets we show that for the family of church rosser languages the higman haines sets which are the sets of all scattered subwords of a given language and the sets of all words that contain some word of a given language as a scattered subword cannot be effectively constructed although both these sets are regular for any language this nicely contrasts the result on the effectiveness of the higman haines sets for the family of context free languages the non effectiveness is based on a non recursive trade off result between the language description mechanism of church rosser languages and the corresponding higman haines sets which in turn is also valid for all supersets of the language family under consideration and in particular for the family of recursively enumerable languages finally for the family of regular languages we prove an upper and a matching lower bound on the size of the higman haines sets in terms of nondeterministic finite automata

size biased sampling of poisson point processes and excursions some general formulae are obtained for size biased sampling from a poisson point process in an abstract space where the size of a point is defined by an arbitrary strictly positive function these formulae explain why in certain cases gamma and stable the size biased permutation of the normalized jumps of a subordinator can be represented by a stickbreaking residual allocation scheme defined by independent beta random variables an application is made to length biased sampling of excursions of a markov process away from a recurrent point of its statespace with emphasis on the brownian and bessel cases when the associated inverse local time is a stable subordinator results in this case are linked to generalizations of the arcsine law for the fraction of time spent positive by brownian motion

decidability of involution hypercodes given a finite set x of strings x is a hypercode if a string in x is not a subsequence of any other string in x we consider hypercodes for involution codes which are useful for dna strand design and define an involution hypercode we then tackle the involution hypercode decidability problem that is to determine whether or not a given language is an involution hypercode based on the hypercode properties we design a polynomial runtime algorithm for regular languages we also prove that it is decidable whether or not a context free language is an involution hypercode note that it is undecidable for some other involution codes such as involution prefix codes suffix codes and k intercodes

a valid matern class of cross covariance functions for multivariate random fields with any number of components we introduce a valid parametric family of cross covariance functions for multivariate spatial random fields where each component has a covariance function from a well celebrated matern class unlike previous attempts our model indeed allows for various smoothnesses and rates of correlation decay for any number of vector components we present the conditions on the parameter space that result in valid models with varying degrees of complexity we discuss practical implementations including reparameterizations to reflect the conditions on the parameter space and an iterative algorithm to increase the computational efficiency we perform various monte carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging the application of the proposed multivariate matern model is illustrated on two meteorological datasets temperature pressure over the pacific northwest bivariate and wind temperature pressure in oklahoma trivariate in the latter case our flexi

enlacements du mouvement brownien autour des courbes de l espace limit theorems are proved for the winding numbers of a three dimensional brownian motion around certain curves in space in particular the joint asymptotic distribution of the winding numbers around two curves is obtained this joint distribution generalizes the asymptotic law of the winding numbers of a planar brownian motion around two points which has recently been given by pitman and yor the limiting distributions are closely related to the time spent by a linear brownian motion above and below a multiple of its maximum process proofs rely on stochastic calculus for continuous semi martingales

multivariate max stable spatial processes summary max stable processes allow the spatial dependence of extremes to be modelled and quantified so they are widely adopted in applications for a better understanding of extremes it may be useful to study several variables simultaneously to this end we study the maxima of independent replicates of multivariate processes both in the gaussian and student t cases we define a poisson process construction and introduce multivariate versions of the smith gaussian extreme value the schlather extremal gaussian and extremal t and the brown resnick models we develop inference for the models based on composite likelihoods we present results of monte carlo simulations and an application to daily maximum wind speed and wind gust

self similar fragmentations derived from the stable tree i the basic object we consider is a certain model of continuum random tree called the stable tree we construct a fragmentation process f t t 0 out of this tree by removing the vertices located under height t thanks to a self similarity property of the stable tree we show that the fragmentation process is also self similar the semigroup and other features of the fragmentation are given explicitly asymptotic results are given as well as a couple of related results on continuous state branching processes

coding properties of dna languages the computation language of a dna based system consists of all the words dna strands that can appear in any computation step of the system in this work we define properties of languages which ensure that the words of such languages will not form undesirable bonds when used in dna computations we give several characterizations of the desired properties and provide methods for obtaining languages with such properties the decidability of these properties is addressed as well as an application we consider splicing systems whose computation language is free of certain undesirable bonds and is generated by nearly optimal comma free codes

deterministic generalized automata a generalized automaton ga is a finite automaton where the single transitions are defined on words rather than on single letters generalized automata were considered by k hashiguchi who proved that the problem of calculating the size of a minimal ga is decidable

studies in the history of probability and statistics xlix on the matern correlation family summary handcock stein 1993 introduced the matern family of spatial correlations into statistics as a flexible parametric class with one parameter determining the smoothness of the paths of the underlying spatial field we document the varied history of this family which includes contributions by eminent physical scientists and statisticians

deciding determinism of caterpillar expressions caterpillar expressions have been introduced by bruggemann klein and wood for applications in markup languages caterpillar expressions provide a convenient formalism for specifying the operation of tree walking automata on unranked trees here we give a formal definition of determinism of caterpillar expressions that is based on the language of instruction sequences defined by the expression we show that determinism of caterpillar expressions can be decided in polynomial time

doubly perturbed jump diffusion processes in this paper we study the existence and uniqueness of the solution to a class of doubly perturbed jump diffusion processes with non lipschitz coefficients some well known results are improved and generalized

obtaining shorter regular expressions from finite state automata we consider the use of state elimination to construct shorter regular expressions from finite state automata fas although state elimination is an intuitive method for computing regular expressions from fas the resulting regular expressions are often very long and complicated we examine the minimization of fas to obtain shorter expressions first then we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given fas we prove that we should not eliminate bridge states until we eliminate all non bridge states to obtain shorter regular expressions in addition we suggest heuristics for state elimination that leads to shorter regular expressions based on vertical chopping and horizontal chopping

cross covariance functions for multivariate random fields based on latent dimensions summary the problem of constructing valid parametric cross covariance functions is challenging we propose a simple methodology based on latent dimensions and existing covariance models for univariate random fields to develop flexible interpretable and computationally feasible classes of cross covariance functions in closed form we focus on spatio temporal cross covariance functions that can be nonseparable asymmetric and can have different covariance structures for instance different smoothness parameters in each component we discuss estimation of these models and perform a small simulation study to demonstrate our approach we illustrate our methodology on a trivariate spatio temporal pollution dataset from california and demonstrate that our cross covariance performs better than other competing models

economy of description for single valued transducers abstract in this article questions of economy of description are investigated in connection with single valued finite transducers the following results are shown 1 any single valued real time transducer m with n states can be effectively transformed into an equivalent unambiguous realtime transducer having at most 2n states 2 let m be a single valued real time transducer with n states and output alphabet which is equivalent to some deterministic real time or subsequential transducer m then m can be effectively transformed into such an m having at most 1 2n max 2 2n3i states where i is a local structural parameter of m 3 for any single valued real time transducer m it is decidable in deterministic polynomial time whether or not it is equivalent to some deterministic real time transducer to some subsequential transducer respectively the results 1 3 can be extended to the case where m is not necessarily real time the upper bound in 1 is at most one state off the optimal upper bound any possible improvement of the upper bound in 2 is greater than or equal to 2n 1

simulation of tempered stable levy bridges and its applications we consider tempered stable levy subordinators and develop a bridge sampling method an approximate conditional probability density function pdf given the terminal values is derived with stable index less than one using the double saddlepoint approximation we then propose an acceptance rejection algorithm based on the existing gamma bridge and the inverse gaussian bridge as proposal densities its performance is comparable to existing sequential sampling methods such as devroye 2009 devroye l 2009 random variate generation for exponentially and ploynomially tilted stable distributions acm trans modeling comput simulation 19 4 18 1 20 and hofert 2011 hofert m 2011 sampling exponentially tilted stable distributions acm trans modeling comput simulation 22 1 3 1 11 when generating a fixed number of observations as applications we consider option pricing problems in levy models first we demonstrate the effectiveness of bridge sampling when combined with adaptive sampling under fin

finite automata and unary languages abstract we prove that o e n log n states are sufficient to simulate an n state 1nfa recognizing a unary language by a 1dfa the lower bound is the same similar tight bounds are shown for the simulation of a 2dfa by a 1dfa and a 1nfa we also show that o n 2 states are sufficient and necessary to simulate an n state 1nfa recognizing a unary language by a 2dfa

etude asymptotique des enlacements du mouvement brownien autour des droites de l espace the existence of a joint asymptotic distribution for the windings of a three dimensional brownian motion around a finite number of straight lines is obtained this complements the recent studies by pitman yor and the authors of the joint asymptotic distribution for the windings of planar brownian motion around a finite number of points

spatially varying cross correlation coefficients in the presence of nugget effects summary we derive sufficient conditions for the cross correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects the derived class is valid for anychoiceofcovariancefunctions andyieldssubstantialflexibilitybetweenmultipleprocesses thekeyis to identify the cross correlation coefficient matrix with a contraction matrix which can be either diagonal implying a parsimonious formulation or a fully general contraction matrix yielding greater flexibility but added model complexity we illustrate the approach with a bivariate minimum and maximum temperature dataset in colorado allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations while still yielding a positive definite covariance matrix

random brownian scaling identities and splicing of bessel processes an identity in distribution due to knight for brownian motion is extended in two different ways first by replacing the supremum of a reflecting brownian motion by the range of an unreflected brownian motion and second by replacing the reflecting brownian motion by a recurrent bessel process both extensions are explained in terms of random brownian scaling transformations and brownian excursions the first extension is related to two different constructions of ito s law of brownian excursions due to williams and bismut each involving back to back splicing of fragments of two independent three dimensional bessel processes generalizations of both splicing constructions are described which involve bessel processes and bessel bridges of arbitrary positive real dimension

arcsine laws and interval partitions derived from a stable subordinator levy discovered that the fraction of time a standard one dimensional brownian motion b spends positive before time t has arcsine distribution both for a fixed time when b t 0 almost surely and for t an inverse local time when b t 0 almost surely this identity in distribution is extended from the fraction of time spent positive to a large collection of functionals derived from the lengths and signs of excursions of b away from 0 similar identities in distribution are associated with any process whose zero set is the range of a stable subordinator for instance a bessel process of dimension d for 0 d 2

doubly perturbed neutral stochastic functional equations in this paper we prove the existence and uniqueness of the solution to a class of doubly perturbed neutral stochastic functional equations dpnsfes in short under some non lipschitz conditions the solution is constructed by successive approximation furthermore we give the continuous dependence of the solution on the initial value by means of the corollary of bihari inequality

a lamperti type representation of continuous state branching processes with immigration guided by the relationship between the breadth first walk of a rooted tree and its sequence of generation sizes we are able to include immigration in the lamperti representation of continuous state branching processes we provide a representation of continuous state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent levy processes stability of the solutions is studied and gives in particular limit theorems of a type previously studied by grimvall kawazu and watanabe and by li and a simulation scheme for continuous state branching processes with immigration we further apply our stability analysis to extend pitman s limit theorem concerning galton watson processes conditioned on total population size to more general offspring laws

the sde solved by local times of a brownian excursion or bridge derived from the height profile of a random tree or forest let b be a standard one dimensional brownian motion started at 0 let l t v b be the occupation density of b at level v up to time t the distribution of the process of local times l t v b v 0 conditionally given b 0 and l t 0 b l is shown to be that of the unique strong solution x of the ito sde dx v 4 x 2 a t 0 x v du 1 dv 2 x v dbv on the interval 0 v t x where v t x inf v f v 0 x u du t and x v 0 for all v v t x this conditioned form of the ray knight description of brownian local times arises from study of the asymptotic distribution as n and 2k n l of the height profile of a uniform rooted random forest of k trees labeled by a set of n elements as obtained by conditioning a uniform random mapping of the set to itself to have k cyclic points the sde is the continuous analog of a simple description of a galton watson branching process conditioned on its total progeny for l 0 corresponding to asymptotics of a uniform random tree the sde gives a description of the process of local times of a brownian excursion which is equivalent to jeulin s description of these local times as a time change of twice a brownian excursion another corollary is the biane yor description of the local times of a reflecting brownian ridge as a time changed reversal of twice a brownian meander of the same length

aggregation cokriging for highly multivariate spatial data best linear unbiased prediction of spatially correlated multivariate random processes often called cokriging in geostatistics requires the solution of a large linear system based on the covariance and cross covariance matrix of the observations for many problems of practical interest it is impossible to solve the linear system with direct methods we propose an efficient linear unbiased predictor based on a linear aggregation of the covariables the primary variable together with this single meta covariable is used to perform cokriging we discuss the optimality of the approach under different covariance structures and use it to create reanalysis type high resolution historical temperature fields

perturbed brownian motions we study perturbed brownian motions that can be loosely speaking described as follows they behave exactly as linear brownian motion except when they hit their past maximum or and maximum where they get an extra push we define with no restrictions on the perturbation parameters a process which has this property and show that its law is unique within a certain natural class of processes in the case where both perturbations at the maximum and at the minimum are self repelling we show that in fact more is true such a process can almost surely be constructed from brownian paths by a one to one measurable transformation this generalizes some results of carmona petit yor and davis we also derive some fine properties of perturbed brownian motions hausdorff dimension of points of monotonicity for example

minimal nfa problems are hard finite automata fa s are of fundamental importance in theory and in applications the following basic minimization problem is studied given a dfa deterministic fa find a minimum equivalent no

pathwise uniqueness for perturbed versions of brownian motion and reflected brownian motion any solution of the functional equation wta bta asup st wsa 1 l w t 0 where b is a brownian motion behaves like a reflected brownian motion except when it attains a new maximum we call it an a per turbed reflected brownian motion similarly any solution of xta bta asup st xsa binft xs t 0 behaves like a brownian motion except when it attains a new maxi mum or minimum we call it an a b doubly perturbed brownian motion we complete some recent investigations by showing that for all permissible values of the parameters a a and b respectively these equations have pathwise unique solutions and these are adapted to the filtration of b