共查询到20条相似文献,搜索用时 15 毫秒
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Antoine Lejay 《Journal of Differential Equations》2010,249(8):1777-1798
The theory of rough paths allows one to define controlled differential equations driven by a path which is irregular. The most simple case is the one where the driving path has finite p-variations with 1?p<2, in which case the integrals are interpreted as Young integrals. The prototypal example is given by stochastic differential equations driven by fractional Brownian motion with Hurst index greater than 1/2. Using simple computations, we give the main results regarding this theory - existence, uniqueness, convergence of the Euler scheme, flow property … - which are spread out among several articles. 相似文献
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We develop the rough path counterpart of Itô stochastic integration and differential equations driven by general semimartingales. This significantly enlarges the classes of (Itô/forward) stochastic differential equations treatable with pathwise methods. A number of applications are discussed. 相似文献
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Atsushi Takeuchi 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(5):711-736
Consider stochastic functional differential equations, whose coefficients depend on past histories. The solution determines a non-Markov process. In the present paper, we shall obtain the existence of smooth densities for joint distributions of solutions, under the uniformly elliptic condition on the diffusion coefficients, via the Malliavin calculus. As an application, we shall study the computations of the Greeks on options associated with the asset price dynamics models with delayed effects. 相似文献
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《Stochastic Processes and their Applications》2020,130(5):2639-2674
Given a stochastic differential equation with path-dependent coefficients driven by a multidimensional Wiener process, we show that the support of the law of the solution is given by the image of the Cameron–Martin space under the flow of mild solutions to a system of path-dependent ordinary differential equations. Our result extends the Stroock–Varadhan support theorem for diffusion processes to the case of SDEs with path-dependent coefficients. The proof is based on functional Itô calculus. 相似文献
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David Nualart Lluís Quer-Sardanyons 《Stochastic Processes and their Applications》2009,119(11):3914-3938
In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d≥1 and d≤3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. 相似文献
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Yulin SONG 《Frontiers of Mathematics in China》2018,13(1):161-172
We consider a real-valued doubly-perturbed stochastic differential equation driven by a subordinated Brownian motion. By using classic Malliavin calculus, we prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure on . 相似文献
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《Stochastic Processes and their Applications》2020,130(10):6445-6479
We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes. 相似文献
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The main goal of this paper is to solve fractional differential equations by means of an operational calculus. Our calculus is based on a modified shift operator which acts on an abstract space of formal Laurent series. We adopt Weyl’s definition of derivatives of fractional order. 相似文献
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In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential equations.We theoretically prove that the schemes have second-order convergence rate.To demonstrate the effectiveness and the second-order convergence rate,numerical tests are given. 相似文献
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Seiichiro Kusuoka 《Journal of Functional Analysis》2010,258(3):758-784
I considered if solutions of stochastic differential equations have their density or not when the coefficients are not Lipschitz continuous. However, when stochastic differential equations whose coefficients are not Lipschitz continuous, the solutions would not belong to Sobolev space in general. So, I prepared the class Vh which is larger than Sobolev space, and considered the relation between absolute continuity of random variables and the class Vh. The relation is associated to a theorem of N. Bouleau and F. Hirsch. Moreover, I got a sufficient condition for a solution of stochastic differential equation to belong to the class Vh, and showed that solutions of stochastic differential equations have their densities in a special case by using the class Vh. 相似文献
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《Applied Mathematical Modelling》2014,38(11-12):3031-3037
In ordinary differential equation (ODE) and stochastic differential equation (SDE), the solution continuously depends on initial value and parameter under some conditions. This paper investigates the analogous continuous dependence theorems in uncertain differential equation (UDE). It proves two continuous dependence theorems, a basic one and a general one. 相似文献
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Qian Lin 《数学学报(英文版)》2013,29(5):923-942
In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness and comparison theorems for those stochastic differential equations with non-Lipschitz coefficients are obtained. 相似文献
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《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):303-330
In this paper we show that the solution of an anticipating stochastic differential equation with smooth coefficients and with a random and smooth initial condition possesses an infinitely differentiable density under some non-degeneracy conditions 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(4):830-841
This paper introduces an estimation method based on Least Squares Support Vector Machines (LS-SVMs) for approximating time-varying as well as constant parameters in deterministic parameter-affine delay differential equations (DDEs). The proposed method reduces the parameter estimation problem to an algebraic optimization problem. Thus, as opposed to conventional approaches, it avoids iterative simulation of the given dynamical system and therefore a significant speedup can be achieved in the parameter estimation procedure. The solution obtained by the proposed approach can be further utilized for initialization of the conventional nonconvex optimization methods for parameter estimation of DDEs. Approximate LS-SVM based models for the state and its derivative are first estimated from the observed data. These estimates are then used for estimation of the unknown parameters of the model. Numerical results are presented and discussed for demonstrating the applicability of the proposed method. 相似文献
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In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous
spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be
equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued
mild solution to a general second order stochastic partial differential equation driven by such a noise. For this, we apply
the techniques of the Malliavin calculus. Our results apply to the case of the stochastic heat equation in any space dimension
and the stochastic wave equation in space dimension d=1,2,3. Moreover, for these particular examples, known results in the literature have been improved.
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In this article we investigate the equivalence of underdetermined differential equations and differential equations with deviations
of second order with respect to the pseudogroup of transformations = φ(x), ȳ = ȳ() = L(x) + y(x), = () = M(x) + z(x). Our main aim is to determine such equations that admit a large pseudogroup of symmetries. Instead the common direct calculations,
we use some more advanced tools from differential geometry, however, our exposition is self-contained and only the most fundamental
properties of differential forms are employed.
This research has been conducted at the Department of Mathematics as part of the research project CEZ: Progressive reliable
and durable structures, MSM 0021630519. 相似文献