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作者：Ekren, Ibrahim; Keller, Christian; Touzi, Nizar; Zhang, Jianfeng
作者单位：University of Southern California; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional Ito calculus recently introduced by Dupire [Functional Ito calculus (2009...
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作者：Tsirelson, Boris
作者单位：Tel Aviv University
摘要：A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of sigma-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of sigma-fields. The largest extension of such Boolean algebra of sigma-fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.
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作者：Jara, M.; Landim, C.; Teixeira, A.
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：Consider a sequence of possibly random graphs G(N) = (V-N, E-N), N >= 1, whose vertices's have i.i.d. weights {W-x(N) : x is an element of V-N} with a distribution belonging to the basin of attraction of an alpha-stable law, 0 < alpha < 1. Let X-t(N), t >= 0, be a continuous time simple random walk on G(N) which waits a mean W-x(N) exponential time at each vertex x. Under considerably general hypotheses, we prove that in the ergodic time scale this trap model converges in an appropriate topolo...
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作者：Buckdahn, Rainer; Li, Juan; Quincampoix, Marc
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Shandong University
摘要：In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study for such a game the problem of the existence of a value without Isaacs condition. Not surprising, this requires a suitable concept of mixed strategies which, to the authors' best knowledge, was not known in the context of stochastic differential games. For this, we consider nonan...
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作者：Panchenko, Dmitry
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed p-spin models for even p >= 2 was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed p-spin models which also include p-spin interactions for odd p. Most of the ideas used in the paper are well known and can now be combined following a recent proof of the Parisi ultrametricity conjecture in.
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作者：Basdevant, Anne-Laure; Schapira, Bruno; Singh, Arvind
作者单位：Universite Paris Nanterre; Universite Paris Saclay; Universite Paris Saclay
摘要：We characterize nondecreasing weight functions for which the associated one-dimensional vertex reinforced random walk (VRRW) localizes on 4 sites. A phase transition appears for weights of order n log log n: for weights growing faster than this rate, the VRRW localizes almost surely on, at most, 4 sites, whereas for weights growing slower, the VRRW cannot localize on less than 5 sites. When w is of order n log log n, the VRRW localizes almost surely on either 4 or 5 sites, both events happenin...
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作者：Cuny, Christophe; Merlevede, Florence
作者单位：Universite Paris Saclay; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in H (a real and separable Hilbert space) admits an approximation, in L-p (H), p > 1, by a martingale with stationary differences, and we then estimate the error of approximation in L-p (H). The results are exploited to further investigate the behavior of the partial sums. In particular we obtain new projective conditions concerning the Marcinkiewicz-Z...
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作者：Einmahl, Uwe; Kuelbs, Jim
作者单位：Vrije Universiteit Brussel; University of Wisconsin System; University of Wisconsin Madison
摘要：Let X, X-1, X-2,... be i.i.d, mean zero random vectors with values in a separable Banach space B, S-n = X-1 +...+ X-n for n >= 1, and assume {c(n) : n >= 1} is a suitably regular sequence of constants. Furthermore, let S((n)) (t), 0 <= t <= 1 be the corresponding linearly interpolated partial sum processes. We study the cluster sets A = C({S-n/c(n)}) and A = C({S((n))(.)/c(n)}). In particular, A and A are shown to be nonrandom, and we derive criteria when elements in B and continuous functions...
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作者：Castell, Fabienne; Guillotin-Plantard, Nadine; Pene, Francoise; Schapira, Bruno
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bretagne Occidentale; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：Random walks in random scenery are processes defined by Z(n) := Sigma(n)(k=1) xi(X1+ ...+Xk), where basically (X-k, k >= 1) and (xi(y), y is an element of Z) are two independent sequences of i.i.d. random variables. We assume here that X-1 is Z-valued, centered and with finite moments of all orders. We also assume that xi(0) is Z-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that (n(-3/4)Z([nt]), t >= 0) converges in distribution as n --> infinity toward ...
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作者：Wang, Feng-Yu
作者单位：Beijing Normal University; Swansea University
摘要：A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move together as soon as possible, for the new-type coupling the two marginal processes start from the same point but their difference is aimed to reach a fixed quantity at a given time. Besides the integration by parts formula, the new coupling method is also efficient...
