共查询到20条相似文献,搜索用时 140 毫秒
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We develop the Euler–Maruyama scheme for a class of stochastic differential equations with Markovian switching (SDEwMSs) under non-Lipschitz conditions . Both L1 and L2-convergence are discussed under different non-Lipschitz conditions. To overcome the mathematical difficulties arisen from the Markovian switching as well as the non-Lipschitz coefficients, several new analytical techniques have been developed in this paper which should prove to be very useful in the numerical analysis of stochastic systems. 相似文献
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We study the Kepler problem perturbed by an anisotropic term, that is a potential conformed by a Newtonian term, 1/r, plus an anisotropic term, b/(r2[1+?cos2θ])β/2. Because of the anisotropic term, although the system is conservative the angular momentum is not a constant of motion. 相似文献
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Pullback attractors of non-autonomous stochastic degenerate parabolic equations on unbounded domains
This paper is concerned with pullback attractors of the stochastic p -Laplace equation defined on the entire space Rn. We first establish the asymptotic compactness of the equation in L2(Rn) and then prove the existence and uniqueness of non-autonomous random attractors. This attractor is pathwise periodic if the non-autonomous deterministic forcing is time periodic. The difficulty of non-compactness of Sobolev embeddings on Rn is overcome by the uniform smallness of solutions outside a bounded domain. 相似文献
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The truncated variation, TVc, is a fairly new concept introduced in ?ochowski (2008) [5]. Roughly speaking, given a càdlàg function f, its truncated variation is “the total variation which does not pay attention to small changes of f, below some threshold c>0”. The very basic consequence of such approach is that contrary to the total variation, TVc is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in ?ochowski (2011) [6], another characterization of TVc has been found. Namely TVc is the smallest possible total variation of a function which approximates f uniformly with accuracy c/2. Due to these properties we envisage that TVc might be a useful concept both in the theory and applications of stochastic processes. 相似文献
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In this paper we connect the well established theory of stochastic differential inclusions with a new theory of set-valued stochastic differential equations. Solutions to the latter equations are understood as continuous mappings taking on their values in the hyperspace of nonempty, bounded, convex and closed subsets of the space L2 consisting of square integrable random vectors. We show that for the solution X to a set-valued stochastic differential equation corresponding to a stochastic differential inclusion, there exists a solution x for this inclusion that is a ‖⋅‖L2-continuous selection of X. This result enables us to draw inferences about the reachable sets of solutions for stochastic differential inclusions, as well as to consider the viability problem for stochastic differential inclusions. 相似文献
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This paper is devoted to presenting a method of proving verification theorems for stochastic optimal control of finite dimensional diffusion processes without control in the diffusion term. The value function is assumed to be continuous in time and once differentiable in the space variable (C0,1) instead of once differentiable in time and twice in space (C1,2), like in the classical results. The results are obtained using a time dependent Fukushima–Dirichlet decomposition proved in a companion paper by the same authors using stochastic calculus via regularization. Applications, examples and a comparison with other similar results are also given. 相似文献
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It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established. 相似文献
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In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h2)-order superconvergence error estimate is established under the conditions of almost uniform partition and the H3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Finally, as an application, the numerical treatment of Maxwell equation is discussed and computational results are presented. 相似文献
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Mario Maurelli 《Comptes Rendus Mathematique》2011,349(11-12):669-672
We prove a uniqueness result for the stochastic transport linear equation (STLE), without any or BV hypothesis on the coefficient, which is needed for the corresponding deterministic equation. We use Wiener chaos decomposition to pass from the STLE to a deterministic second-order transport equation with uniqueness property. 相似文献
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A fundamental problem in computer science is that of finding all the common zeros of m quadratic polynomials in n unknowns over F2. The cryptanalysis of several modern ciphers reduces to this problem. Up to now, the best complexity bound was reached by an exhaustive search in 4log2n2n operations. We give an algorithm that reduces the problem to a combination of exhaustive search and sparse linear algebra. This algorithm has several variants depending on the method used for the linear algebra step. We show that, under precise algebraic assumptions on the input system, the deterministic variant of our algorithm has complexity bounded by O(20.841n) when m=n, while a probabilistic variant of the Las Vegas type has expected complexity O(20.792n). Experiments on random systems show that the algebraic assumptions are satisfied with probability very close to 1. We also give a rough estimate for the actual threshold between our method and exhaustive search, which is as low as 200, and thus very relevant for cryptographic applications. 相似文献
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In this paper, we study nonconforming finite element method for stochastic Stokes equation driven by white noise. We apply “green function framework” and standard duality technique to study the error estimate for velocity in L2-norm and for pressure in H-1-norm. Finally, numerical experiment proves our theoretical results. 相似文献
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We investigate a stochastic evolution equation for the motion of a second grade fluid filling a bounded domain of R2. Global existence and uniqueness of strong probabilistic solution is established. In contrast to previous results on this model we show that the sequence of Galerkin approximation converges in mean square to the exact strong probabilistic solution of the problem. We also give two results on the long time behavior of the solution. Mainly we prove that the strong solution of our stochastic model converges exponentially in mean square to the stationary solution of the time-independent second grade fluids equations if the deterministic part of the external force does not depend on time. If the deterministic forcing term explicitly depends on time, then the strong probabilistic solution decays exponentially in mean square. 相似文献