共查询到20条相似文献,搜索用时 15 毫秒
1.
《Journal de Mathématiques Pures et Appliquées》1999,78(9):877-894
The formula of integration by parts for heat measures over a loop group established by B. Driver is revesited through an alternative approach to this result. We shall first establish directly the integration by parts formula over an unimodular Lie group (which will be the finite product of a compact Lie group with a correlated metric), using the concept of tangent processes. A new expression for Ricci tensor will enable us the passage to the limit. 相似文献
2.
I. Camilier 《Journal of Functional Analysis》2010,259(1):268-300
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated situation encountered in Poisson models. We establish a quasi-invariance result: we show that if atom locations are perturbed along a vector field, the resulting process is still a determinantal (respectively permanental) process, the law of which is absolutely continuous with respect to the original distribution. Based on this formula, following Bismut approach of Malliavin calculus, we then give an integration by parts formula. 相似文献
3.
We establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et?al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147?C235, 1983) fails. 相似文献
4.
Chull Park David Skoug David Storvick 《Rendiconti del Circolo Matematico di Palermo》1998,47(2):277-292
In this paper we complete the following four objectives: 1. We obtain an integration by parts formula for analytic Feynman
integrals. 2. We obtain an integration by parts formula for Fourier-Feynman transforms. 3. We find the Fourier-Feynman transform
of a functionalF from a Banach algebra
after it has been multiplied byn linear factors. 4. We evaluate the analytic Feynman integral of functionals like those described in 3 above. A very fundamental
result by Cameron and Storvick [5, Theorem 1], in which they express the analytic Feynman integral of the first variation
of a functionalF in terms of the analytic Feynman integral ofF multiplied by a linear factor, plays a key role throughout this paper. 相似文献
5.
6.
A hybrid method for simulations of cooling processes of high quality glass is investigated. The hybrid algorithm relies on two solvers or the radiative transfer equation and on a global error estimator which allows for an optimal choice of the solver in each frequency band. The global error estimator is formulated in a general Hilbert space setting. Abstract formulations of a Gauss‐like integration‐by‐parts formula and its inversion are required. 相似文献
7.
Oana Mocioalca 《Journal of Functional Analysis》2005,222(2):385-434
We extend the Skorohod integral, allowing integration with respect to Gaussian processes that can be more irregular than any fractional Brownian motion. This is done by restricting the class of test random variables used to define Skorohod integrability. A detailed analysis of the size of this class is given; it is proved to be non-empty even for Gaussian processes which are not continuous on any closed interval. Despite the extreme irregularity of these stochastic integrators, the Skorohod integral is shown to be uniquely defined, and to be useful: an Ito formula is established; it is employed to derive a Tanaka formula for a corresponding local time; linear additive and multiplicative stochastic differential equations are solved; an analysis of existence for the stochastic heat equation is given. 相似文献
8.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1999,328(11):1061-1066
A Girsanov formula and an integration by parts formula are given for quantum stochastic processes on the Heisenberg-Weyl algebra and used to obtain sufficient conditions for their Wigner density in a given state to lie in the Sobolev space of order k. 相似文献
9.
In this paper, we focus on the characterization for fractional Brownian bridge measures. We give the integration by parts formula for such measures by Bismut''s method and their pull back formula. Conversely, we prove that such measures can be determined through their integration by parts formula. 相似文献
10.
H. Zessin 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(1):50-58
A fundamental theorem of Mürmann [2] characterizing equilibrium distributions of physical clusters is reconsidered. We recover
this result by means of the integration by parts formula approach to Gibbs processes due to Nguyen Xuan Xanh and Hans Zessin
[4].
Dedicated to Reinhard Lang on the occasion of his 60 th birthday. 相似文献
11.
We prove stochastic Fubini theorem for general stable measure which will be used to develop some identities in law for functionals of one and two-parameter stable processes. This result is subsequently used to establish the integration by parts formula for stable sheet. 相似文献
12.
Masanori Hino 《Journal of Functional Analysis》2010,258(5):1656-1681
In Euclidean space, the integration by parts formula for a set of finite perimeter is expressed by the integration with respect to a type of surface measure. According to geometric measure theory, this surface measure is realized by the one-codimensional Hausdorff measure restricted on the reduced boundary and/or the measure-theoretic boundary, which may be strictly smaller than the topological boundary. In this paper, we discuss the counterpart of this measure in the abstract Wiener space, which is a typical infinite-dimensional space. We introduce the concept of the measure-theoretic boundary in the Wiener space and provide the integration by parts formula for sets of finite perimeter. The formula is presented in terms of the integration with respect to the one-codimensional Hausdorff-Gauss measure restricted on the measure-theoretic boundary. 相似文献
13.
Shaoqin ZHANG 《Frontiers of Mathematics in China》2016,11(2):461-496
Shift Harnack inequality and integration by parts formula are established for semilinear stochastic partial differential equations and stochastic functional partial differential equations by modifying the coupling used by F.-Y. Wang [Ann. Probab., 2012, 42(3): 994–1019]. Log-Harnack inequality is established for a class of stochastic evolution equations with non-Lipschitz coefficients which includes hyperdissipative Navier-Stokes/Burgers equations as examples. The integration by parts formula is extended to the path space of stochastic functional partial differential equations, then a Dirichlet form is defined and the log-Sobolev inequality is established. 相似文献
14.
Giuseppe Da Prato Arnaud Debussche Beniamin Goldys 《Probability Theory and Related Fields》2002,123(3):355-380
We consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms.
We prove an integration by part formula and a Logarithmic Sobolev inequality for the invariant measure. No symmetry or reversibility
assumptions are made. Furthemore we prove some compactness results on the transition semigroup and on the embedding of the
Sobolev spaces based on the invariant measure. We use these results to derive asymptotic properties for a stochastic reaction–diffusion
equation.
Received: 29 September 2000 / Revised version: 30 May 2001 / Published online: 14 June 2002 相似文献
15.
Acta Mathematicae Applicatae Sinica, English Series - In this paper we investigate an integration by parts formula for Lévy processes by using lower bound conditions of the corresponding... 相似文献
16.
Ivan Nourdin 《Journal of Functional Analysis》2010,258(11):3775-3791
We combine infinite-dimensional integration by parts procedures with a recursive relation on moments (reminiscent of a formula by Barbour (1986)), and deduce explicit expressions for cumulants of functionals of a general Gaussian field. These findings yield a compact formula for cumulants on a fixed Wiener chaos, virtually replacing the usual “graph/diagram computations” adopted in most of the probabilistic literature. 相似文献
17.
In this paper we develop an unconditionally stable third order time integration formula for the diffusion equation with Neumann boundary condition. We use a suitable arithmetic average approximation and explicit backward Euler formula and then develop a third order L-stable Simpson’s 3/8 type formula. We also observe that the arithmetic average approximation is not unique. Then L-stable Simpson’s 3/8 type formula and Hopf-Cole transformation is used to solve Burger’s equation with Dirichlet boundary condition. It is also observed that this numerical method deals efficiently in case of inconsistencies in initial and boundary conditions. 相似文献
18.
We derive a Wick–Itô formula, that is, an Itô-type formula based on Wick integration. We derive it in the context of regular Gaussian processes which include Brownian motion and fractional Brownian motion with Hurst parameter greater than 1/2. We then consider applications to the Black and Scholes formula for the pricing of a European call option. It has been shown that using Wick integration in this context is problematic for economic reasons. We show that it is also problematic for mathematical reasons because the resulting Black and Scholes formula depends only on the variance of the process and not on its dependence structure. 相似文献
19.
本文研究分数扩散过程和其分部积分公式的关系.首先利用Bismut方法给出拉回公式,进而得到分数扩散过程的分部积分公式。反过来,证明了分数扩散过程可由其分部积分公式唯一刻画. 相似文献
20.
V. I. Rodionov 《Differential Equations》2013,49(6):662-679
We define a special multiplication of function series (skew multiplication) and a generalized Riemann-Stieltjes integral with function series as integration arguments. The generalized integrals and the skew multiplication are related by an integration by parts formula. The generalized integrals generate a family of linear generalized integral equations, which includes a family (represented in integral form via the Riemann-Stieltjes integral) of linear differential equations with several deviating arguments. A specific feature of these equations is that all deviating functions are defined on the same closed interval and map it into itself. This permits one to avoid specifying the initial functions and imposing any additional constraints on the deviating functions. We present a procedure for constructing the fundamental solution of a generalized integral equation. With respect to the skew multiplication, it is invertible and generates the product of the fundamental solution (a function of one variable) by its inverse function (a function of the second variable). Under certain conditions on the parameters of the equation, the product has all specific properties of the Cauchy function. We introduce the notion of adjoint generalized integral equation, obtain a representation of solutions of the original equation and the adjoint equation in generalized integral Cauchy form, and derive sufficient conditions for the convergence of solutions of a pair of adjoint equations. 相似文献