excessive measures and the existence of right semigroups and processes given a resolvent u on a lusin space e f the paper gives necessary and sufficient conditions in terms of the excessive measures that ensure the existence of a right process resp a right continuous semigroup on e f with resolvent u furthermore a notion of nonbranch points with respect to un is introduced also in terms of the excessive measures and various characterizations are given they show in particular the equivalence of this definition with those introduced and discussed by engelbert and wittmann

general gauge and conditional gauge theorems general gauge and conditional gauge theorems are established for a large class of not necessarily symmetric strong markov processes including brownian motions with singular drifts and symmetric stable processes furthermore new classes of functions are introduced under which the general gauge and conditional gauge theorems hold these classes are larger than the classical kato class when the process is brownian motion in a bounded c 1 1 domain

excursions of dual processes there has been considerable interest in the excursions of a markov process in recent years perhaps the most important general result is that of maisonneuve 13 in which the existence of an exit system is established this general result was applied to the study of specific excursions by getoor in 5 then maisonneuve recast and generalized these results in 14 where he showed how to discuss the excursion straddling a certain class of stopping times t these included the excursion straddling a fixed time and the first excursion whose length exceeds a given value which were discussed in 5 the purpose of this paper is to study excursions for processes which satisfy duality conditions a start in this direction was made in section 10 of 5 under assumptions that were much too strong it turns out that the appropriate duality hypotheses are stronger than those of classical duality as described in i we assume the existence of dual transition densities rather than the weaker assumption of dual potential kernel densities our precise assumptions are described in section 2 and especially in section 3 in particular it is shown in these sections that a systematic use of space time processes obviates the need for any regularity assumptions on the density over and above the chapman kolmogorov equation section 4 summarizes the special properties of additive functionals under our hypotheses that are needed in later sections in theorem 4 5 we show that if m is a closed homogeneous optional set then under duality assumptions there exists a borel set f c e e such that me3 0 and t 0 xt xt f are indistinguishable in section 5 we begin the discussion of excursions from a closed homogeneous optional set m with r i n f t 0 t c m if f e e corresponds to m as above r inf t xt art f almost surely especially important is 5 17 which gives the joint distribution of r x r and x r this is obtained by applying a reversal argument to the excursion

stopping distributions for right processes letx be a transient right process for which semipolar sets are polar we characterize the measures which can arise as the distribution ofx t witht a non randomized stopping time

critical dynamics of phase transition driven by dichotomous markov noise an ising spin system under the critical temperature driven by a dichotomous markov noise magnetic field with a finite correlation time is studied both numerically and theoretically the order parameter exhibits a transition between two kinds of qualitatively different dynamics symmetry restoring and symmetry breaking motions as the noise intensity is changed there exist regions called channels where the order parameter stays for a long time slightly above its critical noise intensity developing a phenomenological analysis of the dynamics we investigate the distribution of the passage time through the channels and the power spectrum of the order parameter evolution the results based on the phenomenological analysis turn out to be in quite good agreement with those of the numerical simulation

on optimal performance of nonlinear energy sinks in multiple degree of freedom systems abstract we study the problem of optimizing the performance of a nonlinear spring mass damper attached to a class of multiple degree of freedom systems we aim to maximize the rate of one way energy transfer from primary system to the attachment and focus on impulsive excitation of a two degree of freedom primary system with an essentially nonlinear attachment the nonlinear attachment is shown to be able to perform as a nonlinear energy sink nes by taking away energy from the primary system irreversibly for some types of impulsive excitations using perturbation analysis and exploiting separation of time scales we perform dimensionality reduction of this strongly nonlinear system our analysis shows that efficient energy transfer to nonlinear attachment in this system occurs for initial conditions close to homoclinic orbit of the slow time scale undamped system a phenomenon that has been previously observed for the case of single degree of freedom primary systems analytical formulae for optimal parameters for given impulsive excitation input are derived generalization of this framework to systems with arbitrary number of degrees of freedom of the primary system is also discussed the performance of both linear and nonlinear optimally tuned attachments is compared while nes performance is sensitive to magnitude of the initial impulse our results show that nes performance is more robust than linear tuned mass damper to several parametric perturbations hence our work provides evidence that homoclinic orbits of the underlying hamiltonian system play a crucial role in efficient nonlinear energy transfers even in high dimensional systems and gives new insight into robustness of systems with essential nonlinearity

markov properties of multiparameter processes and capacities we study a class of multiparameter symmetric markov processes we prove that this class is stable by subordination in bochner s sense we show then that for these processes a probabilistic and an analytic potential theory correspond to each other in particular additive functionals are associated with finite energy measures hitting probabilities are estimated by capacities quasicontinuity corresponds to path continuity in the last section examples show that many earlier results as well as new ones in this domain can be obtained by our method

positive solutions of systems of semilinear elliptic equations the pendulum method abstract conditions are formulated which guarantee the existence of positive solutions for simultaneous systems on an open domain with each constant is a positive measure the main tools used are probabilistic potential theory markov processes and an iterative scheme which is not a generalization of the one used for quasi monotone systems quasi monotonicity is not assumed and new results are obtained

potential theoretic nature of hardy s inequality for dirichlet forms we prove that the hardy inequality for dirichlet forms of symmetric markov processes recently proved by p j fitzsimmons can be established within the framework of our potential inequality this clearly emphasizes the role played by the maximum principle in the inequality

on the quasi regularity of non sectorial dirichlet forms by processes having the same polar sets abstract we obtain a criterion for the quasi regularity of generalized non sectorial dirichlet forms which extends the result of p j fitzsimmons on the quasi regularity of sectorial semi dirichlet forms given the right markov process associated to a semi dirichlet form we present sufficient conditions for a second right process to be a standard one having the same state space the above mentioned quasi regularity criterion is then an application the conditions are expressed in terms of the associated capacities nests of compacts polar sets and quasi continuity the second application is on the quasi regularity of the generalized dirichlet forms obtained by perturbing a semi dirichlet form with kernels

excessive measures and markov processes with random birth and death on utilise un processus markovien continu a droite stationnaire defini sur un intervalle de temps aleatoire comme outil naturel pour developper plusieurs aspects de la theorie des mesures excessives

excessive kernels and revuz measures we consider a proper submarkovian resolvent of kernels on a lusin measurable space and a given excessive measure with every quasi bounded excessive function we associate an excessive kernel and the corresponding revuz measure every finite measure charging no polar set is such a revuz measure provided the hypothesis b of hunt holds under a weak duality hypothesis we prove the revuz formula and characterize the quasi boundedness and the regularity in terms of revuz measures we improve results of azema 2 and getoor and sharpe 20 for the natural additive functionals of a borel right process

gaugeability and conditional gaugeability new kato classes are introduced for general transient borel right processes for which gauge and conditional gauge theorems hold these new classes are the genuine extensions of the green tight measures in the classical brownian motion case however the main focus of this paper is on establishing various equivalent conditions and consequences of gaugeability and conditional gaugeability we show that gaugeability conditional gaugeability and the subcriticality for the associated schrodinger operators are equivalent for transient borel right processes with strong duals analytic characterizations of gaugeability and conditional gaugeability are given for general symmetric markov processes these analytic characterizations are very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases connections with the positivity of the spectral radii of the associated schrodinger operators are also established

snakes and spiders brownian motion on ℝ trees we consider diffusion processes on a class of trees the processes are defined in a manner similar to that of le gall s brownian snake each point in the tree has a real valued height or generation and the height of the diffusion process evolves as a brownian motion when the height process decreases the diffusion retreats back along a lineage whereas when the height process increases the diffusion chooses among branching lineages according to relative weights given by a possibly infinite measure on the family of lineages the class of trees we consider can have branch points with countably infinite branching and lineages along which the branch points have points of accumulation

return map analysis of chaotic phase synchronization we investigate chaotic phase synchronization cps observed in a mutually coupled map system and a forced map oscillator by using return maps rm of phase difference rm visualizes the presence or absence of the channel for phase slip which characterizes the onset of cps it is found that cps occurs when the channel starts to be completely closed and that the saddle node point is approximately equal to the point at which the channel is closed on the average furthermore the proposed rm describes the critical characteristics of the phase difference and reveals the existence of the quasi synchronized state below the synchronization point

cone paths for the planar brownian snake for the brownian path valued process of le gall or brownian snake in bbb r 2 the times at which the process is a cone path are considered as a function of the size of the cone and the terminal position of the path the results show that the paths for the path valued process have local properties unlike those of a standard brownian motion

on the n back and forth types of boolean algebras the objective of this paper is to uncover the structure of the back and forth equivalence classes at the nite levels for the class of boolean algebras as an application we obtain bounds on the computational complexity of determining the back and forth equivalence classes of a boolean algebra for nite levels this result has implications for characterizing the relatively intrinsically 0 relations of boolean algebras as existential formulas over a nite set of relations

riesz decompositions in markov process theory riesz decompositions of excessive measures and excessive functions are obtained by probabilistic methods without regularity assumptions the decomposition of excessive measures is given for borel right processes the results for excessive functions are formulated within the framework of weak duality these results extend and generalize the pioneering work of hunt in this area

one point extensions of markov processes by darning this paper is a continuation of the works by fukushima tanaka ann inst henri poincare probab stat 41 419 459 2005 and chen fukushima ying stochastic analysis and application p 153 196 the abel symposium springer heidelberg on the study of one point extendability of a pair of standard markov processes in weak duality in this paper general conditions to ensure such an extension are given in the symmetric case characterizations of the one point extensions are given in terms of their dirichlet forms and in terms of their l2 infinitesimal generators in particular a generalized notion of flux is introduced and is used to characterize functions in the domain of the l2 infinitesimal generator of the extended process an important role in our investigation is played by the order approaching probability u

subordination in the wide sense for levy processes given t t 0 a transient convolution semigroup over rd we characterize the transient semi groups which are subordinate in the wide sense to the latter via some quotient relation between the two levy generators this is also equivalent to an inclusion between excessive cones thanks to a theorem of hirsch this allows us in big dimensions to give a probabilistic description of some measures satisfying the classical maximum principle

capacity theory without duality the paper develops a theory of capacity for a borel right process without duality assumptions the basic tool in this approach is a stationary process ralative to an excessive measure ifp t t 0 denotes the semigroup of the process on the state spacee and ifm is an excessive measure one then there exists a processy y t t one with random birth and death and a finite measureq m such thaty is stationary underq m and markov with respect to p t for a setb ine the hitting resp last exit time ofy is denoted by b resp b andb is called transient resp cotransient ifq m b 0 resp q m b 0 the main theorem then states that for a both transient and contransient setb the distributions of b and b underq m are the same for suchb the capacity is denfined byc b q m b 0 1 and the cocapacity by hat c b q m b 0 1 and it is shown that these definitions in fact generalize previous definitions under duality assumptions without duality assumption there is no representation of the capacitary potential in terms of a capacitary measure but there exists a cocapacitary entrance law which generalizes the notion of a cocapacitary measure such that hat c b mathop sup limits t 0 1 the paper contains investigations of transience and cotransience a decomposition of the cocapacitrary entrance law some remarks on left versions and furthermore a generalization of spitzer s asymptotic formula

absolute continuity of symmetric markov processes we study girsanov s theorem in the context of symmetric markov processes extending earlier work of fukushima takeda and fitzsimmons on girsanov transformations of gradient type we investigate the most general girsanov transformation leading to another symmetric markov process this investigation requires an extension of the forward backward martingale method of lyons zheng to cover the case of processes with jumps

brownian excursions from hyperplanes and smooth surfaces on obtient une decomposition en produit gauche de la loi d excursion brownienne a n dimensions n 2 a partir d un hyperplan

realizing hybrid synchronization of time delay hyperchaotic 4d systems via partial variables hybrid synchronization of time delay hyperchaotic 4d systems with different initial conditions is investigated via partial variables based on the lyapunov stability theory sufficient conditions are given to get the hybrid synchronization by constructing a novel lyapunov function in the form of exponential form it is proved that some partial state variables of two time delay hyperchaotic systems are anti synchronized while other state variables are complete synchronized when one or two linear controllers are imposed on the response system simultaneously the unknown parameters in the response system are also estimated completely numerical simulation results are presented to demonstrate the effectiveness of the proposed chaos synchronization scheme

killing a markov process under a stationary measure involves creation on construit la mesure de kuznetsov associee a une mesure excessive m et le semigroupe d un processus tue selon une fonctionnelle multiplicative m en termes de la mesure de kuznetsov correspondant a m

conditional gauge theorem for non local feynman kac transforms feynman kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of markov processes general gauge and conditional gauge theorems are established for such transforms furthermore the l 2 infinitesimal generator of the schrodinger semigroup given by a non local feynman kac transform is determined in terms of its associated bilinear form

dynamical models for circle covering brownian motion and poisson updating we consider two dynamical variants of dvoretzky s classical problem of random interval coverings of the unit circle the latter having been completely solved by l shepp in the first model the centers of the intervals perform independent brownian motions and in the second model the positions of the intervals are updated according to independent poisson processes where an interval of length l is updated at rate l where 0 is a parameter for the model with brownian motions a special case of our results is that if the length of the nth interval is c n then there are times at which a fixed point is not covered if and only if c 2 and there are times at which the circle is not fully covered if and only if c 3 for the poisson updating model we obtain analogous results with c and c 1 instead we also compute the hausdorff dimension of the set of exceptional times for some of these questions

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

some zero one laws for additive functionals of markov processes let xt px be anm symmetric markov process with a strictly positive transition density consider the additive functionalat 0tf xs wheref e 0 is a universally measurable function on the state spacee among others we prove thatpx at 0 already impliespx at 0 the latter is also equivalent topx at 0 for quasi everyx e and allt 0 and to the analytic condition smallint f n fdm infty for a sequence of finely open borel setsfn such thate fn is polar in the special cases of brownian motion and bessel process these results were obtained earlier by h j engelbert w schmidt x x xue and the authors

boolean algebra approximations knight and stob proved that every low4 boolean algebra is 0 6 isomorphic to a computable one furthermore for n 1 2 3 4 every lown boolean algebra is 0 n 2 isomorphic to a computable one we show that this is not true for n 5 there is a low5 boolean algebra that is not 0 7 isomorphic to any computable boolean algebra it is worth remarking that because of the machinery developed the proof uses at most a 0 00 priority argument the technique used to construct this boolean algebra is new and might be useful in other applications such as to solve the lown boolean algebra problem either positively or negatively

symmetries of excessive measures of markov processes our goal in this article is to study one aspect of a classical problem in markov process theory namely when is a function y t of a markov process y t once again a markov process we discuss an algorithm for constructing a large class of such functions based upon the potential theory of y t we study the symmetries of the excessive measures of y t from the results it is clear that a large amount of the structure of the process y t is embedded in the algebraic structure of the symmetries

a discontinuous time change for natural additive functionals which preserves duality continuous time changes of markov processes preserve duality but a discontinuous time change recently proposed by weidenfeld does not we modify his procedure to obtain a time change which preserves duality when the time changing functional is natural

finely harmonic functions of a markov process let x be a borel right process and m a fixed excessive measure given a finely open nearly borel set g we define an operator g which we regard as an extension of the restriction to g of the generator of x it maps functions on e to locally signed measures on g not charging m semipolars given a locally smooth signed measure we define h to be finely harmonic on g provided g h 0 on g and denote the class of such h by h f g under mild conditions on x we show that h h f g is equivalent to a local poisson representation of h we characterize h f g by an analog of the mean value property under secondary assumptions we obtain global poisson type representations and study the dirichlet problem for elements of h f g under suitable finiteness hypotheses the results take their nicest form when specialized to hunt processes

stationary regenerative sets and subordinators abstract this paper gives a simple construction of the general stationary regenerative set based on the stationary version of the associated subordinator increasing levy process it is shown that in a certain sense the closed range of such a levy process is a stationary regenerative subset of r the distribution of this regenerative set is delta finite in general it is finite if the increments of the levy process have finite expectation

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

hardy s inequality for dirichlet forms abstract we prove an abstract form of hardy s l2 inequality in which the dirichlet integral is replaced by the dirichlet form of a general symmetric markov process a number of examples are provided

on the equivalence of three potential principles for right markov processes we examine three of the principles of probabilistic potential theory in a nonclassical setting these are i the bounded maximum principle ii the positive definiteness of the energy of measures of bounded potential and iii the condition that each semipolar set is polar these principles are known to be equivalent in the context of two markov processes in strong duality when excessive functions are lower semicontinuous we show that when the principles are appropriately formulated their equivalence persists in the wider context of a borel right markov processx with distinguished excessive measurem we make no duality hypotheses andm need not be a reference measure our main tools are the stationary process y qm associated withx andm and a correspondence between potentials u and certain random measures over y qm

symmetry groups and translation invariant representations of markov processes the symmetry groups of the potential theory of a markov process xt are used to introduce new algebraic and topological structures on the state space and the process for example let g be the collection of bijections sp on e which preserve the collection of excessive functions assume there is a transitive subgroup h of the symmetry group g such that the only map 9 e h fixing a point e e e is the identity map on e there is a bijection p e h so that the algebraic structure of h can be carried to e making e into a group if there is a left quasi invariant measure on e then there is a topology on e making e into a locally compact second countable metric group there is also a time change r t of xt such that xt t is a translation invariant process on e and xt t is right continuous with left limits in the new topology

non symmetric perturbations of symmetric dirichlet forms abstract we provide a path space integral representation of the semigroup associated with the quadratic form obtained by lower order perturbation of a symmetric local dirichlet form the representation is a combination of feynman kac and girsanov formulas and extends previously known results in the framework of symmetric diffusion processes through the use of the hardy class of smooth measures which contains the kato class of smooth measures

trace operator and the dirichlet problem for elliptic equations on arbitrary bounded open sets abstract we consider the dirichlet problem and the weak dirichlet problem on a general possibly nonregular bounded domain for elliptic linear equation with uniformly elliptic divergence form operator we investigate carefully the relationship between weak integral probabilistic soft and the perron wiener brelot solutions of the problem we also study the relationship between solutions of the dirichlet problem and weak dirichlet problem to this end we extend the usual notion of the trace operator and consider the dirichlet problem with martin boundary

wiener s test for super brownian motion and the brownian snake we prove a wiener type criterion for super brownian motion and the brownian snake if f is a borel subset of d and x d we provide a necessary and sufficientcondition for super brownian motion started at x to immediately hit the set f equivalently this condition is necessary and sufficient for the hitting time of f by thebrownian snake with initial point x to be 0 a key ingredient of the proof isan estimate showing that the hitting probability of f is comparable up to multiplicative constants to the relevant capacity of f this estimate which is of independent interest refines previous results due to perkins and dynkin an important role is played by additivefunctionals of the brownian snake which are investigated here via the potentialtheory of symmetric markov processes as a direct application of our probabilisticresults we obtain a necessary and sufficient condition for the existence in a domain d of a positivesolution of the equation u u 2 which explodes at a given point of d

on the potential theory of symmetric markov processes on reprend des resultats de dynkin et on considere un processus de markov fort symetrique continu a droite on etudie la relation existant entre le cone de mesures positives d energie finie et la capacite

an application of flows to time shift and time reversal in stochastic processes a simple proposition theorem 1 on flows allows the investigation of random time shift and time reversal in markov processes without assuming any regularity of paths theorem 5 is a generalization of nagasawa s time reversal theorem and theorem 4 generalizes a recent result of getoor and glover 1 flows 1 1 we consider a flow in a measurable space 2 y that is a family of transformations at t e r such that oat 0s t for all s t e r and t c oto e a e r x 4 for all a e f r is the borel a algebra in r we put oty x y otw for every function y and pot a p 0t71a a e y p pot dt for every measure p we denote by the collection of all sets a e y such that t1a a for all t e r a function y is measurable with respect to the a algebra wif and only if it is measurable and invariant under all transformations ot obviously p a 0 or oo for all a e sl nevertheless we prove theorem 1 if p is a finite over y it determines uniquely the values p a for all a e 1 2 as a tool we use stationary times a stationary time t is a measurable mapping from 2 to the extended real line oo oo such that ott t t for all t e r suppose that y coincides with its completion with respect to the class of all probability measures then the first hitting time of a set a e y ta inf t ot e a and the last exit time from a ta sup t ot co a are stationary times2 the measurability follows from 5 chapter 3 1 received by the editors march 13 1984 1980 mathematics subject classification primary 60g 601 1 supported in part by national science foundation grant mcs 8202286 2we put inf oo sup oo c1985 american mathematical society 0002 9947 85 1 00 25 per page

regenerative embedding of markov sets given a closed markov i e regenerative set in 0 we characterize the laws of the markov sets which are regeneratively embedded into the latter typically let 1 and 2 be two laplace exponents corresponding to two regenerative laws and m 2 a markov set with exponent 2 there exists a markov set m 1 with exponent 1 which is regeneratively embedded into m 2 if and only if 1 2 is a completely monotone function several examples and applications are discussed

sub markovian resolvents under weak duality hypothesis we study the weak duality between two sub markovian resolvents of kernels on a lusin topological space with respect to a given measure m our frame covers the probabilistic context of two borel markov processes in weak duality the main results are related to the coincidence of the m semipolar and m cosemipolar sets the revuz correspondence between the measures charging no cofinely open m polar set and the potential kernels associated with the homogeneous random measures of the process the equivalence between smoothness and cosmoothness a smooth measure is the revuz measure of a continuous additive functional we extend and improve results of r m blumenthal r k getoor j azema d revuz j b walsh r k getoor m j sharpe

markov processes and nonsymmetric dirichlet forms without regularity we study right markov processes in weak duality satisfying the sector condition of silverstein dirichlet space techniques are employed but without the customary c0 regularity hypothesis nonetheless the potential theory of such processes is quite amenable in particular it is proved that semipolar sets are quasi polar this extends results of silverstein and lejan

a computability theoretic equivalent to vaught s conjecture we prove that for every theory t which is given by an l 1 sentence t has less than 2 0 many countable models if and only if we have that for every x 2 on a cone of turing degrees every x hyperarithmetic model of t has an x computable copy we also find a concrete description relative to some oracle of the turing degree spectra of all the models of a counterexample to vaught s conjecture

green s and dirichlet spaces associated with fine markov processes this is the second paper in a series devoted to green s and dirichlet spaces in the first paper we have investigated green s space k and the dirichlet space h associated with a symmetric markov transition function pt x b now we assume that p is a transition function of a fine markov process x and we prove that a the space h can be built from functions which are right continuous along almost all paths b the positive cone k in k can be identified with a cone m of measures on the state space c the positive cone h in h can be interpreted as the cone of green s potentials of measures m to every measurable set b in the state space e there correspond a subspace k b of k and a subspace h b of h the orthogonal projections of k onto k and of h onto h b can be expressed in terms of the hitting probabilities of b by the markov process x as the main tool we use additive functionals of x corresponding to measures m

on harris recurrence in continuous time we show that a continuous time markov process x is harris recurrent if and only if there exists a nonzero finite measure i on its state space such that x surely hits sets with positive i measure this simple criterion is applied to some nonparametric closed queueing networks

chaotic phase synchronization and phase diffusion critical behaviors after the breakdown of chaotic phase synchronization in coupled two chaotic oscillators are studied by observing phase diffusion for phase difference of the oscillators particularly by paying attention to similarity and difference of the critical behavior of the angular velocity

drift transforms and green function estimates for discontinuous processes in this paper we consider girsanov transforms of pure jump type for discontinuous markov processes we show that under some quite natural conditions the green functions of the girsanov transformed process are comparable to those of the original process as an application of the general results the drift transform of symmetric stable processes is studied in detail in particular we show that the relativistic a stable process in a bounded c 1 1 smooth open set d can be obtained from symmetric a stable process in d through a combination of a pure jump girsanov transform and a feynman kac transform from this we deduce that the green functions for these two processes in d are comparable

recursive labelling systems and stability of recursive structures in hyperarithmetical degrees we show that under certain assumptions of recursiveness in 2t the recursive structure 2t is ao stable for ca w we need to deal with limit ordinals and we frame an analogous result proposition 2 for yn systems where yn is an increasing sequence of ordinals propositions 1 and 2 are then established by the

continuum sites stepping stone models coalescing exchangeable partitions and random trees analogues of stepping stone models are considered where the sitespace is continuous the migration process is a general markov process and the type space is infinite such processes were defined in previous work of the second author by specifying a feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing markov processes an alternative representation is obtained here in terms of a limit of interacting particle systems it is shown that under a mild condition on the migration process the continuum sites stepping stone process has continuous sample paths the case when the migration process is brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating brownian motion this duality relation is also used to show that a tree like random compact metric space that is naturally associated to an in nite family of coalescing brownian motions on the circle has hausdorff and packing dimension both almost surely equal to 1 2 and moreover this space is capacity equivalent to the middle 1 2 cantor set and hence also to the brownian zero set

a class of path valued markov processes and its applications to superprocesses let s be a continuous markov process satisfying certain regularity assumptions we introduce a path valued strong markov process associated with s which is closely related to the so called superprocess with spatial motion s in particular a subseth of the state space of s intersects the range of the superprocess if and only if the set of paths that hith is not polar for the path valued process the latter property can be investigated using the tools of the potential theory of symmetric markov processes a set is not polar if and only if it supports a measure of finite energy the same approach can be applied to study sets that are polar for the graph of the superprocess in the special case when s is a diffusion process we recover certain results recently obtained by dynkin

homogeneous random measures and a weak order for the excessive measures of a markov process let x xt px be a right markov process and let m be an excessive measure for x associated with the pair x m is a stationary strong markov process yt qm with random times of birth and death with the same transition function as x and with m as one dimensional di stribution we use yt qm to study the cone of excessive measures for x a weak order is defined on this cone an excessive measure is weakly dominated by m if and only if there is a suitable homogeneous random measure tt such that yt q6 is obtained by birthing yt qm birth in t t dt occurring at rate s dt random measures such as s are studied through the use of palm measures we also develop aspects of the general theory of processes over yt qm including the moderate markov property of yt qm when the arrow of time is reversed applications to balayage and capacity are suggested

on the excursions of markov processes in classical duality on obtient des resultats comparables a ceux de getoor et sharpe 1982 sous des hypotheses de dualite classique

strongly supermedian kernels and revuz measures in the frame of borel right markov processes we investigate following an analytical point of view the revuz correspondence between classes of potential kernels and their associated measures improving upon the results of revuz azema getoor and sharpe fitzsimmons fitzsimmons and getoor and dellacherie maisonneuve and meyer in the probabilistic approach of the problem the kernels that occur are the potential operators of different types of homogeneous random measures we completely characterize the hypothesis b of hunt in terms of revuz measures