the true self repelling motion we construct and study a continuous real valued random process which is of a new type it is self interacting self repelling but only in a local sense it only feels the self repellance due to its occu pation time measure density in the immediate neighbourhood of the point it is just visiting we focus on the most natural process with these properties that we call true self repelling motion this is the continuous counterpart to the integer valued true self avoiding walk which had been studied among others by the first author one of the striking properties of true self repelling motion is that although the coupleoxt occupation time measure of x at time tu is a continuous markov process x is not driven by a stochastic diaerential equation and is not a semi martingale it turns out for instance that it has a finite variation of order 3 2 which contrasts with the finite quadratic variation of semi martingales one of the key tools in the construction of x is a continuous system of coalescing brownian motions similar to those that have been constructed by arratia a1 a2 we derive various properties of x existence and properties of the occupation time densities ltoxu local variation etc and an identity that shows that the dynamics of x can be very loosely speaking described as follows dxt is equal to the gradient in space of ltoxu in a gener alized sense even though x7 ltoxu is not diaerentiable

on the dziok srivastava operator under multivalent analytic functions abstract the aim of this paper is to investigate various properties and characteristics of the dziok srivastava operator introduced in dziok and srivastava j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 our paper is motivated essentially by the familiar work liu and srivastava j l liu h m srivastava certain properties of the dziok srivastava operator appl math comput 159 2004 485 493 which has been recently published

inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for the generalized hypergeometric function and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

mouvement brownien cones et processus stables letw wt t 0 denote a two dimensional brownian motion starting at 0 and for 0 4 here we construct a measure a local time supported onh for 4 2 the brownian motionw time changed by the inverse of this local time is shown to be a two dimensional stable process with index 2 2 this results extends spitzer s construction of the cauchy process which is recovered by taking 2 a formula which describes the behaviour ofw before a timet h is established and applied to the proof of a conjecture of burdzy we also obtain a two dimensional version of the famous theorem of levy concerning the maximum process of linear brownian motion precisely for 0 2 letst denote the vertex of the smallest wedge of the typez c which contains the path ofw up to timet the processst wt is shown to be a reflected brownian motion in the wedgec with oblique reflection on the sides finally we investigate various extensions of the previous results to brownian motion inrd d 3 letc be the cone associated with an open subset of the spheresd 1 and leth be defined ash above sufficient conditions are given forh to contain nonzero times in terms of the first eigenvalue of the dirichlet laplacian on

une extension des theoremes de ray et knight sur les temps locaux browniens we introduce two classes of random variablesv such that the brownian local time process at timev is distributed as a 0 or 2 dimensional bessel bridge moreover we obtain new decompositions of the brownian path on the interval 0 v which generalize williams results

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

tilting modules and auslander s gorenstein property abstract the notion of generalized tilting modules is introduced over arbitrary rings it is shown that many results on tilting modules over artin algebras are naturally generalized the auslander s gorenstein property for tilting modules is considered over noetherian rings

tame generalized canonical algebras abstract recently a new wide class of finite dimensional algebras whose auslander reiten quivers admit infinite families of faithful standard stable tubes called generalized canonical algebras has been introduced in a skowronski colloq math 90 2001 77 93 we give a complete description of all tame generalized canonical algebras and prove that all these algebras have tame derived categories of bounded complexes

on certain applications of the hadamard product abstract in this paper we give an extension of the ozkan and altintas results o ozkan o altintas applications of differential subordination appl math lett 19 2006 728 734 on the inclusion relationships involving various subclasses of analytic and univalent functions defined in terms of linear operators we show that these classes are closed under convolution with convex functions

some applications of differential subordination and the dziok srivastava convolution operator abstract by making use of the principle of differential subordination and the dziok srivastava convolution operator we introduce and investigate three interesting subclasses of analytic and univalent functions in the open unit disk we obtain their inclusion relationships and also show that these classes are closed under convolution with convex functions the results presented in this paper provide generalizations of several recent works by for example ozkan and altintas 2006 16 trojnar spelina 2008 30 and many other authors

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

on some applications of the briot bouquet differential subordination recently srivastava et al j dziok h m srivastava certain subclasses of analytic functions associated with the generalized hypergeometric function integral transforms spec funct 14 2003 7 18 j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 y c kim h m srivastava fractional integral and other linear operators associated with the gaussian hypergeometric function complex var theory appl 34 1997 293 312 introduced and studied a class of analytic functions associated with the generalized hypergeometric function in the present paper by using the briot bouquet differential subordination new results in this class are obtained

inclusion relations and convolution properties of a certain class of analytic functions associated with the ruscheweyh derivatives abstract let a denote the class of functions f z with f 0 f 0 1 0 which are analytic in the open unit disk u by means of the ruscheweyh derivatives we introduce and investigate the various properties and characteristics of a certain two parameter subclass t h of a where 0 1 and h z is analytic and convex univalent in u with h 0 1 in particular some inclusion relations and convolution properties for the function class t h are presented here

generalized hypergeometric functions associated with k uniformly convex functions abstract for a certain linear operator which is defined by means of the hadamard product or convolution with a generalized hypergeometric function the authors aim at investigating various mapping and inclusion properties involving such subclasses of analytic and univalent functions as for example k uniformly convex functions and k starlike functions relevant connections of the definitions and results presented in this paper with those in several earlier works on the subject are also pointed out

limiting behaviour of the occupation of wedges by complex brownian motion we prove a theorem which gives the lim inf behaviour ast tends to 0 for the amount of time a complex brownian motion spends in a wedge with apex at the origin the result is then shown to hold uniformly for all wedges a s

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

on the occupation times of cones by brownian motion we study some features concerning the occupation timeat of a d dimensional conec by brownian motion in particular in the case wherec is convex we investigate the asymptotic behaviour ofp a1 u asu 0 when the brownian motion starts at the vertex ofc we also give the precise integral test which decides whether a s lim inft at tf t 0 or for a decreasing functionf

criteria for univalence of the dziok srivastava and the srivastava wright operators in the class a abstract in the geometric function theory gft much attention is paid to various linear integral operators mapping the class s of the univalent functions and its subclasses into themselves in 12 13 hohlov obtained sufficient conditions that guarantee such mappings for the operator defined by means of hadamard product with the gauss hypergeometric function in our earlier papers as 20 19 17 18 etc we extended his method to the operators of the generalized fractional calculus gfc 16 these operators have product functions of the forms m 1 f m and m 1 m and integral representations by means of the meijer g and fox h functions here we propose sufficient conditions that guarantee mapping of the univalent respectively of the convex functions into univalent functions in the case of the celebrated dziok srivastava operator 8 j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 no 1 1999 pp 1 13 defined as a hadamard product with an arbitrary generalized hypergeometric function p f q similar conditions are suggested also for its extension involving the wright p q function and called the srivastava wright operator srivastava 36 since the discussed operators include the above mentioned gfc operators and many their particular cases operators of the classical fc from the results proposed here one can derive univalence criteria for many named operators in the gft as the operators of hohlov carlson and shaffer saigo libera bernardi erdelyi kober etc by giving particular values to the orders p q 1 of the generalized hypergeometric functions and to their parameters

subordinations for analytic functions defined by the dziok srivastava linear operator in the present investigation we obtain certain sufficient conditions for a normalized analytic function f z defined by the dziok srivastava linear operator h l a1 to satisfy the certain subordination our results extend corresponding previously known results on starlikeness convexity and close to convexity

certain properties of the dziok srivastava operator the main object of the present paper is to investigate several interesting properties and characteristics of a linear operator h p q s a 1 which was recently introduced and studied in a series of papers by dziok and srivastava appl math comput 103 1999 1 13 adv stud contemp math 5 2002 115 125 integral transform spec funct 14 2003 7 18 the various properties and characteristics of the linear operator h p q s a 1 which are considered in this paper are associated with for example the principle of differential subordination between analytic functions and a certain one parameter family of integral operators

tilting functors and stable equivalences for selfinjective algebras 1 exta t t 0 2 ext t 0 3 there is a short exact sequence 0 a t t 0 with t t being direct sums of summands of t then putting b end t we call b t a and hom t mod a mod b a tilting triple and a tilting functor respectively tilting functors have been introduced by brenner and butler 6 as a generalization of the bernstein gelfand ponomarev s reflection functors s they and happel and ringel s have proved that we have usually nonhereditary torsion theories f f in mod a and x g in mod b where f xe mod a extj t x 0 and x yemod bi yob t o and the tilting functor and ext t give category equivalences between f and g and between f and x respectively these equivalences give us however no information about indecomposable a modules and b modules which do not belong to the above subcategories f f z and cv the purpose of this paper is to point out that there is a method to enlarge our view by which we can supply the lack of information let us consider trivial extension algebras r a k da and s b k db of a and b by da and db respectively where da hom a k and bdb hom b k are injective cogenerator bimodules in this case r and s are selfinjective more precisely symmetric algebras and mod a and mod b are naturally embedded into projectively stable categories m r and m s then our main theorem states that for any tilting triple

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

neighborhoods of a certain family of multivalent functions with negative coefficients abstract by making use of the familiar concept of neighborhoods of analytic and p valent functions the authors prove coefficient bounds and distortion inequalities and associated inclusion relations for the n neighborhoods of a family of multivalent functions with negative coefficients which is defined by means of a certain nonhomogeneous cauchy euler differential equation relevant connections of the various function classes investigated in this paper with those considered by earlier workers on the subject are also mentioned

classes of multivalent analytic functions involving the dziok srivastava operator the object of the present paper is to investigate some inclusion relationships and a number of other useful properties of several subclasses of multivalent analytic functions which are defined here by using the dziok srivastava operator relevant connections of the results presented here with those obtained in earlier works are pointed out

on the convex combination of the dziok srivastava operator in the paper we obtain the extreme points of some class defined by the dziok srivastava linear operator by using the krein milman theorem some extremal problems in the class are determined

a unified class of k uniformly convex functions defined by the dziok srivastava linear operator abstract the main purpose of this paper is to introduce a new class uh q s k of functions which are analytic in the open unit disk z z c and z 1 we obtain various results including characterization coefficient estimates and distortion and covering theorems for functions belonging to the class uh q s k

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

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

multi self similar markov processes on ℝ n and their lamperti representations a classical result due to lamperti establishes a one to one correspondence between a class of strictly positive markov processes that are self similar and the class of one dimensional levy processes this correspondence is obtained by suitably time changing the exponential of the levy process in this paper we generalise lamperti s result to processes in n dimensions for the representation we obtain it is essential that the same time change be applied to all coordinates of the processes involved also for the statement of the main result we need the proper concept of self similarity in higher dimensions referred to as multi self similarity in the paper

the subleading order of two dimensional cover times the varepsilon cover time of the two dimensional torus by brownian motion is the time it takes for the process to come within distance varepsilon 0 from any point its leading order in the small varepsilon regime has been established by dembo et al ann math 160 433 464 2004 in this work the second order correction is identified the approach relies on a multi scale refinement of the second moment method and draws on ideas from the study of the extremes of branching brownian motion

on constructing stably equivalent functors in this case the left module bt becomes again a generalized tilting module with end t a 8 it should be noted here that the notion of generalized tilting modules is fairly general and the class of such modules contains all tilting modules of finite projective dimension in the sense of miyashita 6 and also all cotilting modules of finite injective dimension especially the injective cogenerator da is always a generalized tilting module even if the regular module a has infinite injective dimension on each side in the joint work with tachikawa 7 we proved the existence of a stably equivalent functor t a t b for any genuine tilting module defined by happel and ringle s by introducing torsion and torsion free resolutions of modules we have tried to generalize the existence