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作者：Bayer, Christian; Schoenmakers, John
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point or more generally with respect to some subset. The representations rely on a reverse process connected with the given (forward) diffusion as introduced in Milstein, Schoenmakers and Spokoiny [Bernoulli 10 (2004) 281-312] in the context of a forward-reverse tr...
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作者：Lucon, Eric; Stannat, Wilhelm
作者单位：Technical University of Berlin
摘要：Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in R-m in the presence of a random environment and with spatial extension: each diffusion is attached to one site of the lattice Z(d), and the interaction between two diffusions is attenuated by a spatial weight that depends on their positions. For a general class of singular weights (including the case already considered ...
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作者：Todorov, Viktor; Tauchen, George
作者单位：Northwestern University; Duke University
摘要：We derive limit theorems for. the empirical distribution function of de-volatilized increments of an Ito semimartingale observed at high frequencies. These devolatilized increments are formed by suitably rescaling and truncating the raw increments to remove the effects of stochastic volatility and large jumps. We derive the limit of the empirical c.d.f. of the adjusted increments for any Ito semimartingale whose dominant component at high frequencies has activity index of 1 < beta <= 2, where ...
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作者：Morris, Ben; Ning, Weiyang; Peres, Yuval
作者单位：University of California System; University of California Davis; University of Washington; University of Washington Seattle; Microsoft
摘要：The card-cyclic-to-random shuffle on n cards is defined as follows: at time t remove the card with label t mod n and randomly reinsert it back into the deck. Pinsky [Probabilistic and combinatorial aspects of the card-cyclic-to-random shuffle (2011). Unpublished manuscript] Introduced this shuffle and asked how many steps are needed to mix the deck. He showed n steps do not suffice. Here we show that the mixing time is on the order of Theta (n log n).
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作者：Spencer, Joel; Sudan, Madhu; Xu, Kuang
作者单位：New York University; Microsoft; Massachusetts Institute of Technology (MIT)
摘要：study an admissions control problem, where a queue with service rate 1 - p receives incoming jobs at rate lambda epsilon (1 - p, 1), and the decision maker is allowed to redirect away jobs up to a rate of p, with the objective of minimizing the time-average queue length. We show that the amount of information about the future has a significant impact on system performance, in the heavy-traffic regime. When the future is unknown, the optimal average queue length diverges at rate similar to log(...
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作者：Dieker, A. B.; Gao, X.
作者单位：University System of Georgia; Georgia Institute of Technology; Chinese University of Hong Kong
摘要：This paper studies diffusion processes constrained to the positive orthant under infinitesimal changes in the drift. Our first main result states that any constrained function and its (left) drift-derivative is the unique solution to an augmented Skorohod problem. Our second main result uses this characterization to establish a basic adjoint relationship for the stationary distribution of the constrained diffusion process jointly with its left-derivative process.
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作者：Douc, Randal; Moulines, Eric; Olsson, Jimmy
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; IMT Atlantique; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT Atlantique; Royal Institute of Technology
摘要：This paper discusses particle filtering in general hidden Markov models (HMMs) and presents novel theoretical results on the long-term stability of bootstrap-type particle filters. More specifically, we establish that the asymptotic variance of the Monte Carlo estimates produced by the bootstrap filter is uniformly bounded in time. On the contrary to most previous results of this type, which in general presuppose that the state space of the hidden state process is compact (an assumption that i...
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作者：Collamore, Jeffrey F.; Dia, Guoqing; Vidyashankar, Anand N.
作者单位：University of Copenhagen; George Mason University
摘要：In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable V satisfying the distributional equation v f (V), where f (v) = A max{v, D} B for (A, B, D) epsilon (0, infinity) X R-2. This paper is concerned with computational methods for evaluating these tail probabilities. We introduce a novel importance sampling algorithm, involving an exponential shift over a random time interval, for estimating...
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作者：Tan, Xiaolu
作者单位：Universite PSL; Universite Paris-Dauphine
摘要：We give a probabilistic interpretation of the Monte Carlo scheme proposed by Fahim, Touzi and Warin [Ann. Appl. Probab. 21 (2011) 1322-1364] for fully nonlinear parabolic PDEs, and hence generalize it to the path-dependent (or non-Markovian) case for a general stochastic control problem. A general convergence result is obtained by a weak convergence method in the spirit of Kushner and Dupuis [Numerical Methods for Stochastic Control Problems in Continuous Time (1992) Springer]. We also get a r...
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作者：Maillard, Pascal; Zeitouni, Ofer
作者单位：Weizmann Institute of Science
摘要：Consider a d-ary rooted tree (d >= 3) where each edge e is assigned an i.i.d. (bounded) random variable X (e) of negative mean. Assign to each vertex v the sum S(v) of X (e) over all edges connecting v to the root, and assume that the maximurn S-n* of S(v) over all vertices v at distance n from the root tends to infinity (necessarily, linearly) as n tends to infinity. We analyze the Metropolis algorithm on the tree and show that under these assumptions there always exists a temperature 1/beta ...
