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1.
2.
Tahir Choulli Christoph Stricker Leszek Krawczyk 《Probability Theory and Related Fields》1999,113(4):571-597
In a previous paper we introduced a new concept, the notion of ℰ-martingales and we extended the well-known Doob inequality
(for 1 < p < + ∞) and the Burkholder–Davis–Gundy inequalities (for p = 2) to ℰ-martingales. After showing new Fefferman-type inequalities that involve sharp brackets as well as the space bmo
q
, we extend the Burkholder–Davis–Gundy inequalities (for 1 < p < + ∞) to ℰ-martingales. By means of these inequalities we give sufficient conditions for the closedness in L
p
of a space of stochastic integrals with respect to a fixed ℝd-valued semimartingale, a question which arises naturally in the applications to financial mathematics. Finally we investigate
the relation between uniform convergence in probability and semimartingale topology.
Received: 22 July 1997 / Revised version: 3 July 1998 相似文献
3.
Nakahiro Yoshida 《Probability Theory and Related Fields》1997,109(3):301-342
Summary. We present an asymptotic expansion of the distribution of a random variable which admits a stochastic expansion around a
continuous martingale. The emphasis is put on the use of the Malliavin calculus; the uniform nondegeneracy of the Malliavin
covariance under certain truncation plays an essential role as the Cramér condition did in the case of independent observations.
Applications to statistics are presented.
Received: 5 September 1995 / In revised form: 20 October 1996 相似文献
4.
Vlad Bally 《Probability Theory and Related Fields》1998,111(3):453-467
Recently the connection between control and game problems and Backward Stochastic Differential Equations has been established.
This allows us to use an approximation scheme for such equations in order to construct an ɛ-optimal control.
Received: 13 November 1995 / Revised version: 11 February 1998 相似文献
5.
Michael Rosier 《Numerische Mathematik》1995,72(2):263-283
Summary.
The concept of singular value decompositions is a valuable tool
in the examination of ill-posed inverse problems
such as the inversion of the Radon transform. A singular value
decomposition depends on the determination of suitable orthogonal systems
of eigenfunctions of the operators
, .
In this paper we consider a new approach which generalizes this concept.
By application of biorthogonal instead of orthogonal functions we
are able to apply a larger class of function sets in order to
account for the structure of the eigenfunction spaces. Although it is
preferable to use eigenfunctions it is still possible to consider
biorthogonal function systems which are not eigenfunctions of the operator.
With respect to the Radon transform for functions with support in the
unit ball we apply the system of Appell polynomials which is a natural
generalization of the univariate system of Gegenbauer (ultraspherical)
polynomials to the multivariate case. The corresponding biorthogonal
decompositions show some advantages in comparison with the known
singular value decompositions. Vice versa by application of our
decompositions we are able to prove new properties of the Appell
polynomials.
Received October 19, 1993 相似文献
6.
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
7.
Yeneng Sun 《Probability Theory and Related Fields》1998,112(3):425-456
For a large collection of random variables in an ideal setting, pairwise independence is shown to be almost equivalent to
mutual independence. An asymptotic interpretation of this fact shows the equivalence of asymptotic pairwise independence and
asymptotic mutual independence for a triangular array (or a sequence) of random variables. Similar equivalence is also presented
for uncorrelatedness and orthogonality as well as for the constancy of joint moment functions and exchangeability. General
unification of multiplicative properties for random variables are obtained. The duality between independence and exchangeability
is established through the random variables and sample functions in a process. Implications in other areas are also discussed,
which include a justification for the use of mutually independent random variables derived from sequential draws where the
underlying population only satisfies a version of weak dependence. Macroscopic stability of some mass phenomena in economics
is also characterized via almost mutual independence. It is also pointed out that the unit interval can be used to index random
variables in the ideal setting, provided that it is endowed together with some sample space a suitable larger measure structure.
Received: 16 April 1997 / Revised version: 18 May 1998 相似文献
8.
Marc Arnaudon 《Probability Theory and Related Fields》1997,108(2):219-257
Summary. We prove that the derivative of a differentiable family X
t
(a) of continuous martingales in a manifold M is a martingale in the tangent space for the complete lift of the connection in M, provided that the derivative is bicontinuous in t and a. We consider a filtered probability space (Ω,(ℱ
t
)0≤
t
≤1, ℙ) such that all the real martingales have a continuous version, and a manifold M endowed with an analytic connection and such that the complexification of M has strong convex geometry. We prove that, given an analytic family a↦L(a) of random variable with values in M and such that L(0)≡x
0∈M, there exists an analytic family a↦X(a) of continuous martingales such that X
1(a)=L(a). For this, we investigate the convexity of the tangent spaces T
(
n
)
M, and we prove that any continuous martingale in any manifold can be uniformly approximated by a discrete martingale up to
a stopping time T such that ℙ(T<1) is arbitrarily small. We use this construction of families of martingales in complex analytic manifolds to prove that
every ℱ1-measurable random variable with values in a compact convex set V with convex geometry in a manifold with a C
1 connection is reachable by a V-valued martingale.
Received: 14 March 1996/In revised form: 12 November 1996 相似文献
9.
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
10.
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
11.
Martin R. Bridson 《Mathematische Annalen》2000,317(4):629-633
Abstract. We construct finitely presented subgroups of GL that have infinitely many conjugacy classes of finite subgroups. This answers a question of Grunewald and Platonov. We suggest
a variation on their question.
Received: 26 August 1999 / Revised: 28 September 1999 / Published online: 8 May 2000 相似文献
12.
13.
In this paper we study the well-posedness and regularity of the adapted solutions to a class of linear, degenerate backward stochastic partial differential equations (BSPDE, for short). We establish new
a priori estimates for the adapted solutions to BSPDEs in a general setting, based on which the existence, uniqueness, and regularity
of adapted solutions are obtained. Also, we prove some comparison theorems and discuss their possible applications in mathematical
finance.
Received: 24 September 1997 / Revised version: 3 June 1998 相似文献
14.
We construct a sequence of branching particle systems α
n
convergent in measure to the solution of the Kushner–Stratonovitch equation. The algorithm based on this result can be used
to solve numerically the filtering problem. We prove that the rate of convergence of the algorithm is of order n
?. This paper is the third in a sequence, and represents the most efficient algorithm we have identified so far.
Received: 4 February 1997 / Revised version: 26 October 1998 相似文献
15.
16.
N. Papamichael I.E. Pritsker E.B. Saff N.S. Stylianopoulos 《Numerische Mathematik》1997,76(4):489-513
Summary. In this paper we examine the convergence rates in an adaptive version of an orthonormalization method for approximating the
conformal mapping of an annular region onto a circular annulus. In particular, we consider the case where has an analytic extension in compl() and, for this case, we determine optimal ray sequences of approximants that give the best possible geometric rate of uniform
convergence. We also estimate the rate of uniform convergence in the case where the annular region has piecewise analytic boundary without cusps. In both cases we also give the corresponding rates for the approximations
to the conformal module of .
Received February 2, 1996 相似文献
17.
18.
We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi [B. Bouchard, N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, The Annals of Applied Probability 10 (3) (2000) 685–708] except that some of the assets can be exchanged freely, i.e. without paying transaction costs. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time. Our proof relies on the introduction of a new auxiliary control problem whose value function can be interpreted as the super-hedging price in a model with unbounded stochastic volatility (in the directions where transaction costs are non-zero). In particular, it confirms the usual intuition that transaction costs play a similar role to stochastic volatility. 相似文献
19.
Benedikt Löwe 《Archive for Mathematical Logic》1998,37(8):505-520
We generalize Solovay's unfolding technique for infinite games and use an Unfolding Theorem to give a uniform method to prove that all analytic
sets are in the -algebras of measurability connected with well-known forcing notions.
Received: 19 July 1996 相似文献
20.
Shige Peng 《Probability Theory and Related Fields》1999,113(4):473-499
We have obtained the following limit theorem: if a sequence of RCLL supersolutions of a backward stochastic differential
equations (BSDE) converges monotonically up to (y
t
) with E[sup
t
|y
t
|2] < ∞, then (y
t
) itself is a RCLL supersolution of the same BSDE (Theorem 2.4 and 3.6).
We apply this result to the following two problems: 1) nonlinear Doob–Meyer Decomposition Theorem. 2) the smallest supersolution
of a BSDE with constraints on the solution (y, z). The constraints may be non convex with respect to (y, z) and may be only measurable with respect to the time variable t. this result may be applied to the pricing of hedging contingent claims with constrained portfolios and/or wealth processes.
Received: 3 June 1997 / Revised version: 18 January 1998 相似文献