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1.
We define stochastic integrals with respect to free Brownian motion, and show that they satisfy Burkholder-Gundy type inequalities
in operator norm. We prove also a version of It?'s predictable representation theorem, as well as product form and functional
form of It?'s formula. Finally we develop stochastic analysis on the free Fock space, in analogy with stochastic analysis
on the Wiener space.
Received: 6 February 1998 相似文献
2.
Multiple fractional integrals 总被引:2,自引:0,他引:2
Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly
identified.
Received: 23 February 1998 / Revised version: 31 July 1998 相似文献
3.
Chaos decomposition of multiple integrals with respect to fractional Brownian motion (with H > 1/2) is given. Conversely the chaos components are expressed in terms of the multiple fractional integrals. Tensor product
integrals are introduced and series expansions in those are considered. Strong laws for fractional Brownian motion are proved
as an application of multiple fractional integrals.
Received: 22 September 1998 / Revised version: 20 April 1999 相似文献
4.
5.
S. Taniguchi 《Probability Theory and Related Fields》1999,114(3):291-308
An evaluation of a stochastic oscillatory integral with quadratic phase function and analytic amplitude function is given
by using solutions of Jacobi equations. The evaluation will be obtained as an application of real change of variable formulas
and holomorphic prolongations of analytic functions on a real Wiener space. On the way we shall see how a Jacobi equation
appears in the evaluation by using the Malliavin calculus.
Received: 27 July 1998 / Revised version: 14 October 1998 相似文献
6.
Summary. We consider a continuous model for transverse magnetization of spins diffusing in a homogeneous Gaussian random longitudinal
field , where is the coupling constant giving the intensity of the random field. In this setting, the transverse magnetization is given
by the formula , where is the standard process of Brownian motion and is the covariance function of the original random field . We use large deviation techniques to show that the limit exists. We also determine the small behavior of the rate and show that it is indeed decaying as conjectured in the physics literature.
Received: 30 June 1995 / In revised form: 26 January 1996 相似文献
7.
Completely positive Markovian cocycles on a von Neumann algebra, adapted to a Fock filtration, are realised as conjugations of -homomorphic Markovian cocycles. The conjugating processes are affiliated to the algebra, and are governed by quantum stochastic differential equations whose coefficients evolve according to the -homomorphic process. Some perturbation theory for quantum stochastic flows is developed in order to achieve the above Stinespring decomposition. Received October 10, 1999 / Revised July 12, 2000 / Published online December 8, 2000 相似文献
8.
Jiongmin Yong 《Probability Theory and Related Fields》1997,107(4):537-572
Summary. The notion of bridge is introduced for systems of coupled forward–backward stochastic differential equations (FBSDEs, for short). This notion
helps us to unify the method of continuation in finding adapted solutions to such FBSDEs over any finite time durations. It is proved that if two FBSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several
classes of uniquely solvable FBSDEs.
Received: 23 April 1996 / In revised form: 10 October 1996 相似文献
9.
By replacing the final condition for backward stochastic differential equations (in short: BSDEs) by a stationarity condition
on the solution process we introduce a new class of BSDEs. In a natural manner we associate to such BSDEs the periodic solution
of second order partial differential equations with periodic structure.
Received: 11 October 1996 / Revised version: 15 February 1999 相似文献
10.
11.
12.
Summary. Given a stochastic action integral we define a notion of invariance of this action under a family of one parameter space-time
transformations and a notion of prolonged transformations which extend the existing analogs in classical calculus of variations.
We prove that a family of prolonged transformations leaves the action integral invariant if and only if it leaves invariant
the heat equation associated to it as well as the structure of the extremals. We then prove a stochastic version of Noether
theorem: to each family of transformations leaving the action invariant (or symmetries) we can associate a function which
gives a martingale when taken along a process minimizing the action under endpoint constraints.
Received: 29 June 1996 / In revised form: 19 July 1996 相似文献
13.
Alexander D. Wentzell 《Probability Theory and Related Fields》1999,113(2):255-271
. For a certain class of families of stochastic processes ηε(t), 0≤t≤T, constructed starting from sums of independent random variables, limit theorems for expectations of functionals F(ηε[0,T]) are proved of the form
where w
0 is a Wiener process starting from 0, with variance σ2 per unit time, A
i
are linear differential operators acting on functionals, and m=1 or 2. Some intricate differentiability conditions are imposed on the functional.
Received: 12 September 1995 / Revised version: 6 April 1998 相似文献
14.
Summary. In this paper, we show the convergence of forms in the sense of Mosco associated with the part form on relatively compact
open set of Dirichlet forms with locally uniform ellipticity and the locally uniform boundedness of ground states under regular
Dirichlet space setting. We also get the same assertion under Dirichlet space in infinite dimensional setting. As a result
of this, we get the weak convergence under some conditions on initial distributions and the growth order of the volume of
the balls defined by (modified) pseudo metric used in K. Th. Sturm.
Received: 18 September 1995 / In revised form: 23 January 1997 相似文献
15.
Xiulin Zou 《Numerische Mathematik》1999,82(3):491-519
The quasi-Laguerre's iteration formula, using first order logarithmic derivatives at two points, is derived for finding roots of polynomials. Three different derivations are presented, each revealing some different properties of the method. For polynomials with only real roots, the method is shown to be optimal, and the global and monotone convergence, as well as the non-overshooting property, of the method is justified. Different ways of forming quasi-Laguerre's iteration sequence are addressed. Local convergence of the method is proved for general polynomials that may have complex roots and the order of convergence is . Received June 30, 1996 / Revised version received August 12, 1996 相似文献
16.
Suppose K is a compact convex set in ℝ2 and X
i
, 1≤i≤n, is a random sample of points in the interior of K. Under general assumptions on K and the distribution of the X
i
we study the asymptotic properties of certain statistics of the convex hull of the sample.
Received: 24 July 1996/Revised version: 24 February 1998 相似文献
17.
Jérôme Dedecker 《Probability Theory and Related Fields》1998,110(3):397-426
Summary. We prove a central limit theorem for strictly stationary random fields under a projective assumption. Our criterion is similar
to projective criteria for stationary sequences derived from Gordin's theorem about approximating martingales. However our
approach is completely different, for we establish our result by adapting Lindeberg's method. The criterion that it provides
is weaker than martingale-type conditions, and moreover we obtain as a straightforward consequence, central limit theorems
for α-mixing or φ-mixing random fields.
Received: 19 February 1997 / In revised form: 2 September 1997 相似文献
18.
Vydas Čekanavičius 《Probability Theory and Related Fields》1998,111(4):565-583
For lattice distributions a convolution of two signed Poisson measures proves to be an approximation comparable with the
normal law. It enables to get rid of cumbersome summands in asymptotic expansions and to obtain estimates for all Borel sets.
Asymptotics can be constructed two-ways: by adding summands to the leading term or by adding summands in its exponent. The
choice of approximations is confirmed by the Ibragimov-type necessary and sufficient conditions.
Received: 20 November 1996 / Revised version: 5 December 1997 相似文献
19.
Miodrag S. Petkovi 'c Carsten Carstensen Miroslav Trajkov ' i c 《Numerische Mathematik》1995,69(3):353-372
Summary.
Classical Weierstrass' formula
[29] has been often the subject of investigation of many
authors. In this paper we give some further
applications of this formula for finding the zeros of polynomials and
analytic functions. We are concerned with the problems of
localization of polynomial zeros and the construction of iterative methods for
the simultaneous approximation and inclusion of these zeros.
Conditions for the safe convergence of Weierstrass' method,
depending only on initial approximations, are given. In particular,
we study polynomials with interval coefficients. Using an interval
version of Weierstrass' method enclosures in the form of disks
for the complex-valued set containing all zeros of a
polynomial with varying coefficients are obtained. We also present
Weierstrass-like algorithm for approximating, simultaneously, all
zeros of a class of analytic functions in a given closed region.
To demonstrate the proposed algorithms, three numerical
examples are included.
Received September 13, 1993 相似文献
20.
G.W. Stewart 《Numerische Mathematik》1994,68(1):143-147
Summary.
This note gives a new convergence proof for iterations based on
multipoint formulas. It rests on the very general assumption that if
the desired fixed point appears as an argument in the formula then
the formula returns the fixed point.
Received March 24, 1993 / Revised version received
January 1994 相似文献