-
作者：Beiglbock, Mathias; Nutz, Marcel; Touzi, Nizar
作者单位：Technische Universitat Wien; Columbia University; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi sure formulation of the dual problem is introduced and shown to yield a complete duality theory for general marginals and measurable reward (cost) functions: absence of a duality gap and existence of dual optimizers. Both properties are shown to fail in the classical formulation. As a consequence of the duality result, we obtain a general princip...
-
作者：Epstein, Charles L.; Pop, Camelia A.
作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
摘要：We study various probabilistic and analytical properties of a class of degenerate diffusion operators arising in population genetics, the so-called generalized Kimura diffusion operators Epstein and Mazzeo [SIAM J. Math. Anal. 42 (2010) 568-608; Degenerate Diffusion Operators Arising in Population Biology (2013) Princeton University Press; Applied Mathematics Research Express (2016)]. Our main results are a stochastic representation of weak solutions to a degenerate parabolic equation with sin...
-
作者：Athreya, Siva; Loehr, Wolfgang; Winter, Anita
作者单位：Indian Statistical Institute; Indian Statistical Institute Bangalore; University of Duisburg Essen
摘要：We consider stochastic processes on complete, locally compact tree-like metric spaces (T,r) on their natural scale with boundedly finite speed measure ?. Given a triple (T,r,nu) such a speed-nu motion on (T,r) can be characterized as the unique strong Markov process which if restricted to compact subtrees satisfies for all x,y is an element of T and all positive, bounded measurable f, E-x[integral(tau y)(0)dsf(X-s)]=2 integral(T)nu(dz)r(y,c(x,y,z))f(z)
-
作者：Banuelos, Rodrigo; Burdzy, Krzysztof; Vares, Maria Eulalia
-
作者：Evans, Steven N.; Gruebel, Rudolf; Wakolbinger, Anton
作者单位：University of California System; University of California Berkeley; Leibniz University Hannover; Goethe University Frankfurt
摘要：Remy's algorithm is a Markov chain that iteratively generates a sequence of random trees in such a way that the nth tree is uniformly distributed over the set of rooted, planar, binary trees with 2n + 1 vertices. We obtain a concrete characterization of the Doob-Martin boundary of this transient Markov chain and thereby delineate all the ways in which, loosely speaking, this process can be conditioned to go to infinity at large times. A (deterministic) sequence of finite rooted, planar, binary...
-
作者：Subag, Eliran
作者单位：Weizmann Institute of Science
摘要：Recently, Auffinger, Ben Arous and Cerny initiated the study of critical points of the Hamiltonian in the spherical pure p-spin spin glass model, and established connections between those and several notions from the physics literature. Denoting the number of critical values less than Nu by Crt(N) (u), they computed the asymptotics of 1/N log(ECrt(N) (u)), as N, the dimension of the sphere, goes to infinity. We compute the asymptotics of the corresponding second moment and show that, for p >= ...
-
作者：Bahlali, Khaled; Eddahbi, M'hamed; Ouknine, Youssef
作者单位：Universite de Toulon; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); King Saud University; Cadi Ayyad University of Marrakech
摘要：We establish a Krylov-type estimate and an Ito-Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This allows us to prove various existence and uniqueness results for some classes of QBSDEs with a square integrable terminal condition and sometimes a merely measurable generator. It turns out that neither the existence of exponential moments of the termin...
-
作者：Friz, Peter K.; Shekhar, Atul
作者单位：Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Indian Statistical Institute; Indian Statistical Institute Bangalore
摘要：We consider rough paths with jumps. In particular, the analogue of Lyons' extension theorem and rough integration are established in a jump setting, offering a pathwise view on stochastic integration against cadlag processes. A class of Levy rough paths is introduced and characterized by a sub-ellipticity condition on the left-invariant diffusion vector fields and a certain integrability property of the Carnot-Caratheodory norm with respect to the Levy measure on the group, using Hunt's framew...
-
作者：Gantert, Nina; Guo, Xiaoqin; Nagel, Jan
作者单位：Technical University of Munich; Purdue University System; Purdue University
摘要：We consider random walk among i.i.d., uniformly elliptic conductances on Z(d), and prove the Einstein relation (see Theorem 1). It says that the derivative of the velocity of a biased walk as a function of the bias equals the diffusivity in equilibrium. For fixed bias, we show that there is an invariant measure for the environment seen from the particle. These invariant measures are often called steady states. The Einstein relation follows at least for d >= 3, from an expansion of the steady s...
-
作者：Marcus, Michael B.; Rosen, Jay
作者单位：City University of New York (CUNY) System; City College of New York (CUNY); City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：An alpha-permanental process {X-t, t is an element of T} is a stochastic process determined by a kernel K = {K (s, t), s, t is an element of T}, with the property that for all t(1),..., t(n) is an element of T, vertical bar I + K(t(1),..., t(n)) S vertical bar(-alpha) is the Laplace transform of (X-t1,...,X-tn), where K (t(1),...,t(n)) denotes the matrix {K(t(i), t(j))}(i,j)(n) = 1 and S is the diagonal matrix with entries s(1),...,s(n). (X-t1,..., X-tn) s called a permanental vector. Under th...
