共查询到20条相似文献,搜索用时 15 毫秒
1.
Kai He 《Bulletin des Sciences Mathématiques》2004,128(2):91-104
In this paper, we prove that the process of the quadratic variation of local times of smooth semimartingales can be constructed as the quasi sure limit of the form ∑Δn(Ltai+1n−Ltain)2, where Δn=(ain,ai+1n) is a sequence of subdivisions of [a,b], ain=i(b−a)/2n+a, i=0,1,…,2n. 相似文献
2.
Summary Consider a stochastic differential equation on
d
with smooth and bounded coefficients. We apply the techniques of the quasi-sure analysis to show that this equation can be solved pathwise out of a slim set. Furthermore, we can restrict the equation to the level sets of a nondegenerate and smooth random variable, and this provides a method to construct the solution to an anticipating stochastic differential equation with smooth and nondegenerate initial condition. 相似文献
3.
Summary A general one dimensional change of variables formula is established for continuous semimartingales which extends the famous Meyer-Tanaka formula. The inspiration comes from an application arising in stochastic finance theory. For functions mapping
n
to , a general change of variables formula is established for arbitrary semimartingales, where the usualC
2 hypothesis is relaxed.Supported in part by NSF grant No. DMS-9103454Supported in part by John D. and Catherine T. MacArthur Foundation award for US-Chile Scientific CooperationSupported in part by FONDECYT, grant 92-0881 相似文献
4.
Vladimir I. Bogachev Michael Röckner Byron Schmuland 《Probability Theory and Related Fields》1996,105(2):193-225
Summary We construct and study generalized Mehler semigroups (p
t
)
t
0 and their associated Markov processesM. The construction methods for (p
t
)
t
0 are based on some new purely functional analytic results implying, in particular, that any strongly continuous semigroup on a Hilbert spaceH can be extended to some larger Hilbert spaceE, with the embeddingHE being Hilbert-Schmidt. The same analytic extension results are applied to construct strong solutions to stochastic differential equations of typedX
t
=C dW
t
+AX
t
dt (with possibly unbounded linear operatorsA andC onH) on a suitably chosen larger spaceE. For Gaussian generalized Mehler semigroups (p
t
)
t
0 with corresponding Markov processM, the associated (non-symmetric) Dirichlet forms (E
D(E)) are explicitly calculated and a necessary and sufficient condition for path regularity ofM in terms of (E,D(E)) is proved. Then, using Dirichlet form methods it is shown thatM weakly solves the above stochastic differential equation if the state spaceE is chosen appropriately. Finally, we discuss the differences between these two methods yielding strong resp. weak solutions. 相似文献
5.
We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum, where the latter running supremum process is continuous. Illustrative examples involving local martingales with discontinuous paths are provided. 相似文献
6.
In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution. 相似文献
7.
A characterization of a regular family of semimatingales as a maximal fasmily of processes with respect of which one can define a stochastic line integral with natural continuity properties is given. 相似文献
8.
Through a regularization procedure, a few schemes for approximation of the local time of a large class of continuous semimartingales and reversible diffusions are given. The convergence holds in the ucp sense. In the case of standard Brownian motion, we have been able to bound the rate of convergence in L2, and to establish the a.s. convergence of some of our schemes. 相似文献
9.
Summary As an application of general convergence results for semimartingales, exposed in their book Limit Theorems for Stochastic Processes, Jacod and Shiryaev obtained a fundamental result on the convergence of likelihood ratio processes to a Gaussian limit. We strengthen this result in a quantitative sense and show that versions of the likelihood ratio processes can be defined on the space of the limiting experiment such that we get pathwise almost sure approximations with respect to the uniform metric. The approximations are considered under both sequences of measures, the hypothesisP
n
and the alternative
. A consequence is e.g. an estimate for the speed of convergence in the Prohorov metric. New approximation techniques for stochastic processes are developed.This article was processed by the author using the LATEX style filepljourIm from Springer-Verlag. 相似文献
10.
The joint continuity of Gaussian local times is investigated under conditions strictly weaker than the local nondeterminism. Our conditions are given in terms of the interpolation variances only and they cover the class of Gaussian Markov processes. A new order of infinitesimal in the tail probability of the local time at the origin is obtained. 相似文献
11.
The notion of a separating time for a pair of measures on a filtered space is helpful for studying problems of (local) absolute continuity and singularity of measures. In this paper, we describe a certain canonical setting for continuous local martingales (abbreviated below as CLMs) and find an explicit form of separating times for CLMs in this setting. 相似文献
12.
Chao ChenLitan Yan 《Statistics & probability letters》2011,81(8):1003-1012
13.
In this paper we show that the local time of the Brownian motion belongs to the Sobolev space
for any p2 and 0<<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function with a Wiener integral W(h), and we show that this composition belongs to
, for any >0 and p>1 such that +1/p>1. 相似文献
14.
15.
Let (t∈[0,1]) be the indefinite Skorohod integral on the canonical probability space (Ω,F,P), and let Lt(x) (t∈[0,1], x∈R) be its the generalized local time introduced by Tudor in [C.A. Tudor, Martingale-type stochastic calculus for anticipating integral processes, Bernoulli 10 (2004) 313-325]. We prove that the generalized local time, as function of x, has the same Besov regularity as the Brownian motion, as function of t, under some conditions imposed on the anticipating integrand u. 相似文献
16.
Summary LetL(x, T),xR
d
,TR
+
N
, be the local time of theN-parameter Wiener processW taking values inR
d
. Even in the distribution valued casedd2N,L can be described in a series representation by means of multiple Wiener-Ito integrals. This setting proves to be a good starting point for the investigation of the asymptotic behaviour ofL(x, T) as |x|0 and/orT and of related occupation integrals
asT. We obtain the rates of explosion in laws of the first order, i.e. normalized convergence laws forL(x, T) resp.X
T
(f), and of the second order, i.e. normalized convergence laws forL(x, T)–E(L(x, T)) resp.X
T
(f)–E(X
T
(f)).This research was made during a stay at the LMU in München supported by DAAD 相似文献
17.
In this paper we prove the existence of a continuous local time for an anticipating process which is composed of an indefinite Skorohod integral and an absolutely continuous term.The work of P. Imkeller was done during his visit to the CRM of Barcelona.Partially supported by the DGICYT grant number PB90-0452. 相似文献
18.
T. S. Zhang 《Potential Analysis》1996,5(3):231-240
In this paper we prove that the local time of the solution of a stochastic differential equation exists except for a set of zero capacity. 相似文献
19.
In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a fixed time are smooth in the sense of Malliavin calculus. Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4. 相似文献
20.
In this article we study the exponential behavior of the continuous stochastic Anderson model, i.e. the solution of the stochastic
partial differential equation u(t,x)=1+∫0tκΔxu (s,x) ds+∫0t W(ds,x) u (s,x), when the spatial parameter x is continuous, specifically x∈R, and W is a Gaussian field on R+×R that is Brownian in time, but whose spatial distribution is widely unrestricted. We give a partial existence result of the
Lyapunov exponent defined as limt→∞t−1 log u(t,x). Furthermore, we find upper and lower bounds for lim supt→∞t−1 log u(t,x) and lim inft→∞t−1 log u(t,x) respectively, as functions of the diffusion constant κ which depend on the regularity of W in x. Our bounds are sharper, work for a wider range of regularity scales, and are significantly easier to prove than all previously
known results. When the uniform modulus of continuity of the process W is in the logarithmic scale, our bounds are optimal.
This author's research partially supported by NSF grant no. : 0204999 相似文献