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作者：Beskos, Alexandros; Jasra, Ajay; Kantas, Nikolas; Thiery, Alexandre
作者单位：University of London; University College London; National University of Singapore; Imperial College London
摘要：In several implementations of Sequential Monte Carlo (SMC) methods it is natural and important, in terms of algorithmic efficiency, to exploit the information of the history of the samples to optimally tune their subsequent propagations. In this article we provide a carefully formulated asymptotic theory for a class of such adaptive SMC methods. The theoretical framework developed here will cover, under assumptions, several commonly used SMC algorithms [Chopin, Biometrika 89 (2002) 539-551; Ja...
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作者：Takahashi, Akihiko; Yamada, Toshihiro
作者单位：University of Tokyo; Mitsubishi International Corporation (MIC)
摘要：This paper develops a new efficient scheme for approximations of expectations of the solutions to stochastic differential equations (SDEs). In particular, we present a method for connecting approximate operators based on an asymptotic expansion with multidimensional Malliavin weights to compute a target expectation value precisely. The mathematical validity is given based on Watanabe and Kusuoka theories in Malliavin calculus. Moreover, numerical experiments for option pricing under local and ...
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作者：Penrose, Mathew D.
作者单位：University of Bath
摘要：Consider a graph on n uniform random points in the unit square, each pair being connected by an edge with probability p if the inter-point distance is at most r. We show that as n -> infinity the probability of full connectivity is governed by that of having no isolated vertices, itself governed by a Poisson approximation for the number of isolated vertices, uniformly over all choices of p, r. We determine the asymptotic probability of connectivity for all (p(n), r(n)) subject to r(n) = o(n(-e...
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作者：Cheng, Dan; Xiao, Yimin
作者单位：North Carolina State University; Michigan State University
摘要：Let X = {X (t), t is an element of R-N} be a centered Gaussian random field with stationary increments and X (0) = 0. For any compact rectangle T subset of R-N and u is an element of R, denote by A(u) = {t is an element of T : X (t) >= u} the excursion set. Under X(center dot) is an element of C-2(R-N) and certain regularity conditions, the mean Euler characteristic of A(u), denoted by E{phi(A(u))}, is derived. By applying the Rice method, it is shown that, as u -> infinity, the excursion prob...
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作者：Fernandez, R.; Manzo, F.; Nardi, F. R.; Scoppola, E.; Sohier, J.
作者单位：Utrecht University; Roma Tre University; Eindhoven University of Technology; Eindhoven University of Technology
摘要：We study the asymptotic hitting time tau((n)) of a family of Markov processes X-(n) to a target set G((n)) when the process starts from a trap defined by very general properties. We give an explicit description of the law of X-(n) conditioned to stay within the trap, and from this we deduce the exponential distribution of tau((n).) Our approach is very broad-it does not require reversibility, the target G does not need to be a rare event and the traps and the limit on n can be of very general ...
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作者：Belomestny, Denis; Kraetschmer, Volker
作者单位：University of Duisburg Essen; HSE University (National Research University Higher School of Economics)
摘要：In this work, we consider optimal stopping problems with conditional convex risk measures of the form rho(Phi)(t)(X) = sup(Q is an element of Qt) (E-Q[-X vertical bar F-t] - E[Phi(dQ/dP)vertical bar F-t]), where Phi : [0, infinity[->[0, infinity] is a lower semicontinuous convex mapping and Q(t) stands for the set of all probability measures Q which are absolutely continuous w.r.t. a given measure P and Q = P on F-t. Here, the model uncertainty risk depends on a (random) divergence E[Phi(dQ/dP...
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作者：Hu, Yaozhong; Liu, Yanghui; Nualart, David
作者单位：University of Kansas
摘要：For a stochastic differential equation(SDE) driven by a fractional Brownian motion(fBm) with Hurst parameter H > 1/2, it is known that the existing (naive) Euler scheme has the rate of convergence n(1-2H). Since the limit H -> 1/2 of the SDE corresponds to a Stratonovich SDE driven by standard Brownian motion, and the naive Euler scheme is the extension of the classical Euler scheme for Ito SDEs for H = 1/2, the convergence rate of the naive Euler scheme deteriorates for H -> 1/2. In this pape...
