共查询到20条相似文献,搜索用时 531 毫秒
1.
We will study the following problem.Let X_t,t∈[0,T],be an R~d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σcontaining an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation. 相似文献
2.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1976,28(1):35-48
Summary Let {X
t
} be defined recursively byX
t
=θX
t−1+U
t
(t=1,2, ...), whereX
0=0 and {U
t
} is a sequence of independent identically distributed real random variables having a density functionf with mean 0 and varianceσ
2. We assume that |θ|<1. In the present paper we obtain the bound of the asymptotic distributions of asymptotically median
unbiased (AMU) estimators of θ and the sufficient condition that an AMU estimator be asymptotically efficient in the sense
that its distribution attains the above bound. It is also shown that the least squares estimator of θ is asymptotically efficient
if and only iff is a normal density function.
University of Electro-Communications 相似文献
3.
For ν(dθ), a σ-finite Borel measure on R
d
, we consider L
2(ν(dθ))-valued stochastic processes Y(t) with te property that Y(t)=y(t,·) where y(t,θ)=∫
t
0
e
−λ(θ)(
t
−
s
)
dm(s,θ) and m(t,θ) is a continuous martingale with quadratic variation [m](t)=∫
t
0
g(s,θ)ds. We prove timewise H?lder continuity and maximal inequalities for Y and use these results to obtain Hilbert space regularity for a class of superrocesses as well as a class of stochastic evolutions
of the form dX=AXdt+GdW with W a cylindrical Brownian motion. Maximal inequalities and H?lder continuity results are also provenfor the path process
t
(τ)≗Y(τt∧t).
Received: 25 June 1999 / Revised version: 28 August 2000 /?Published online: 9 March 2001 相似文献
4.
YU JIARONG 《高校应用数学学报(英文版)》1995,10(4):361-366
WEIGHTEDAPPROXIMATIONOFRANDOMFUNCTIONSYUJIARONGAbstract:Let(Ω,A,P)beaprobabilityspace,X(t,ω)arandomfunctioncontinuousinprobab... 相似文献
5.
Cédric Heuchenne Ingrid Van Keilegom 《Annals of the Institute of Statistical Mathematics》2007,59(2):273-297
Consider the polynomial regression model
, where σ2(X)=Var(Y|X) is unknown, and ε is independent of X and has zero mean. Suppose that Y is subject to random right censoring. A new estimation procedure for the parameters β0,...,β
p
is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the
method of Buckley and James (1979, Biometrika, 66, 429–436), but is, unlike the latter method, a noniterative procedure due to nonparametric preliminary estimation of the
conditional regression function. The asymptotic normality of the estimators is established. Simulations are carried out for
both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than
the Buckley–James estimators. The two estimation procedures are also applied to a medical and an astronomical data set. 相似文献
6.
Kamal C. Chanda 《Annals of the Institute of Statistical Mathematics》2003,55(1):69-82
Let {X
t
;t∈ℤ be a strictly stationary nonlinear process of the formX
t
=ε
t
+∑
r=1
∞
W
rt
, whereW
rt
can be written as a functiong
r
(ε
t−1,...ε
t-r-q
), {ε
t
;t∈ℤ is a sequence of independent and identically distributed (i.i.d.) random variables withE|ε1|
g
< ∞ for some γ>0 andq≥0 is fixed integer. Under certain mild regularity conditions ofg
r
and {ε
t
} we then show thatX
1 has a density functionf and that the standard kernel type estimator
baded on a realization {X
1,...,X
n
} from {X
t
} is, asymptotically, normal and converges a.s. tof(x) asn→∞.
The research of this author was partially carried out while he was a research scholar, on a sabbatical leave, at the Department
of Statistics and Probability, Michigan State University. 相似文献
7.
Hans M. Dietz 《Statistical Inference for Stochastic Processes》2001,4(3):249-258
Suppose one observes a path of a stochastic processX = (Xt)t≥0 driven by the equation
dXt=θ a(Xt)dt + dWt, t≥0, θ ≥ 0
with a(x) = x or a(x) = |x|α for some α ∈ [0,1) and given initial condition X
0. If the true but unknown parameter θ0 is positive then X is non-ergodic. It is shown that in this situation a trajectory fitting estimator for θ0 is strongly consistent and has the same limiting distribution as the maximum likelihood estimator, but converges of minor
order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
8.
Khursheed Alam James R. Thompson 《Annals of the Institute of Statistical Mathematics》1973,25(1):57-64
Summary LetX be normally distributed with mean θ and variance σ2. We consider the problem of estimating θ with squared error as the loss function. A priori the true value of θ is known to
be close to θ0, say. Several estimates are considered which might be preferred toX, the unbiased estimate of θ, as their risks are smaller in the neighborhood of θ0. The admissibility of these estimates is discussed in this paper.
This research was supported in part by ONR Grants NR-042-271 and NR-042-283 at Clemson University and Rice University respectively. 相似文献
9.
This paper considers empirical Bayes estimation of the mean θ of the univariate normal densityf
0 with known variance where the sample sizesm(n) may vary with the component problems but remain bounded by
<∞. Let {(θ
n
,X
n
=(X
n,1,...,X
n, m(n)
))} be a sequence of independent random vectors where theθ
n
are unobservable and iidG and, givenθ
n
=θ has densityf
θ
m(n)
. The first part of the paper exhibits estimators for the density of
and its derivative whose mean-squared errors go to zero with rates
and
respectively. LetR
m(n+1)(G) denote the Bayes risk in the squared-error loss estimation ofθ
n+1 usingX
n+1. For given 0<a<1, we exhibitt
n
(X1,...,X
n
;X
n+1) such that
.
forn>1 under the assumption that the support ofG is in [0, 1]. Under the weaker condition that E[|θ|2+γ]<∞ for some γ>0, we exhibitt
n
*
(X
1,...,X
n
;X
n+1) such that
forn>1. 相似文献
10.
Let (X
t
, Y
t
) be a pure jump Markov process: the state X
t
takes real values and the observation Y
t
is a counting process. The two processes are allowed to have common jump times. Let ϕ(X(⋅)) be a functional of the state trajectory restricted to the time interval [0, T] . If we change the infinitesimal parameters and/ or the initial distribution, then we introduce an error in computing the conditional law of ϕ(X(⋅)) given the observation up to time T . In this paper we give an explicit L
1
-bound for this error.
Accepted 9 March 2001. Online publication 20 June 2001. 相似文献
11.
ZHENGZUKANG 《高校应用数学学报(英文版)》1997,12(1):33-38
Let X,i.i.d. and Y1i. i.d. be two sequences of random variables with unknown distribution functions F(x) and G(y) respectively. X, are censored by Y1. In this paper we study the uniform consistency of the Kaplan-Meier estimator under the case ey=sup(t:F(t)<1)>to=sup(t2G(t)<1) The sufficient condition is discussed. 相似文献
12.
Kamal C. Chanda 《Annals of the Institute of Statistical Mathematics》1983,35(1):439-446
Summary LetX
t
, ...,X
n
be random variables forming a realization from a linear process
where {Z
t
} is a sequence of independent and identically distributed random variables with E|Z
t
|<∞ for some ε>0, andg
r
→0 asr→∞ at some specified rate. LetX
1 have a probability density functionf. It is then established that for every realx, the standard kernel type estimator
based onX
t
(1≦t≦n) is, under some general regularity conditions, asymptotically normal and converges a.s. tof(x) asn→∞.
Research was supported in part by the Air Force Office of Scientific Research Grant No. AFOSR-81-0058. 相似文献
13.
Toyoaki Akai 《Annals of the Institute of Statistical Mathematics》1986,38(1):85-99
Summary LetX
i
,i=1,..., p be theith component of thep×1 vectorX=(X
1,X
2,...,X
p
)′. Suppose thatX
1,X
2,...,X
p
are independent and thatX
i
has a probability density which is positive on a finite interval, is symmetric about θ
i
and has the same variance. In estimation of the location vector θ=(θ1, θ2,...,θ
p
)′ under the squared error loss function explicit estimators which dominateX are obtained by using integration by parts to evaluate the risk function. Further, explicit dominating estimators are given
when the distributions ofX
i
′s are mixture of two uniform distributions. For the loss function
such an estimator is also given when the distributions ofX
i
′s are uniform distributions. 相似文献
14.
Summary We give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the
functionF(p
1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p
1,...,pn) for every realt, whereX
i are independent geometric random variables with parametersp
i. A generalization to negative binomial random variables is also presented. 相似文献
15.
Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(X
ε (t)): ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψ_ε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X ε (t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ_ε(u) and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient
law for the simulation of Ψ_ε(u).
AMS Subject Classifications 60F10, 91B30
This work has been partially supported by Murst Project “Metodi Stocastici in Finanza Matematica” 相似文献
16.
V. F. Gaposhkin 《Mathematical Notes》1998,64(3):316-321
The asymptotic behavior asn → ∞ of the normed sumsσn =n
−1 Σ
k
=0n−1
Xk for a stationary processX = (X
n
,n ∈ ℤ) is studied. For a fixedε > 0, upper estimates for P(sup
k≥n
|σ
k
| ≥ε) asn → ∞ are obtained.
Translated fromMatematicheskie Zametki, Vol. 64, No. 3, pp. 366–372, September, 1998. 相似文献
17.
For topological spaces X and Y and a metric space Z, we introduce a new class N( X ×Y, Z ) \mathcal{N}\left( {X \times Y,\,Z} \right) of mappings f: X × Y → Z containing all horizontally quasicontinuous mappings continuous with respect to the second variable. It is shown that, for
each mapping f from this class and any countable-type set B in Y, the set C
B
(f) of all points x from X such that f is jointly continuous at any point of the set {x} × B is residual in X: We also prove that if X is a Baire space, Y is a metrizable compact set, Z is a metric space, and f ? N( X ×Y, Z ) f \in \mathcal{N}\left( {X \times Y,\,Z} \right) , then, for any ε > 0, the projection of the set D
ε
(f) of all points p ∈ X × Y at which the oscillation ω
f
(p) ≥ ε onto X is a closed set nowhere dense in X. 相似文献
18.
Mario Abundo 《Methodology and Computing in Applied Probability》2010,12(3):473-490
It is studied the first-passage time (FPT) of a time homogeneous one-dimensional diffusion, driven by the stochastic differential
equation dX(t) = μ(X(t))dt + σ(X(t)) dB
t
, X(0) = x
0, through b + Y(t), where b > x
0 and Y(t) is a compound Poisson process with rate λ > 0 starting at 0, which is independent of the Brownian motion B
t
. In particular, the FPT density is investigated, generalizing a previous result, already known in the case when X(t) = μt + B
t
, for which the FPT density is the solution of a certain integral equation. A numerical method is shown to calculate approximately
the FPT density; some examples and numerical results are also reported. 相似文献
19.
E. I. Pancheva 《Journal of Mathematical Sciences》1998,92(3):3911-3920
Given an extremal process X: [0,∞)→[0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ
n
=(τ
n
, ξ
n
), n≥1, of time-space changes (max-automorphisms of [0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ
n
-1
○ X ○ τn(t)=Cn(t) V max {ξ
n
-1
○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t)
=
d
Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is
assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments.
Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
20.
A. F. Izé 《Annali di Matematica Pura ed Applicata》1973,96(1):21-39
Summary It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) [(d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying
where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.
Entrata in Redazione il 5 gennaio 1972. 相似文献