共查询到20条相似文献,搜索用时 31 毫秒
1.
Xiong 《Applied Mathematics and Optimization》2003,47(2):151-165
Abstract. We derive a large deviation principle for the optimal filter where the signal and the observation processes take values in
conuclear spaces. The approach follows from the framework established by the author in an earlier paper. The key is the verification
of the exponential tightness for the optimal filtering process and the exponential continuity of the coefficients in the Zakai
equation. 相似文献
2.
J. Xiong 《Applied Mathematics and Optimization》1999,39(3):281-307
We consider an interacting system of n diffusion processes X
n
j
(t): t∈[0,1] , j=1,2,. . ., n , taking values in a conuclear space Φ' . Let ζ
n
t
=(1/n)Σ
n
j=1
δ
Xnj(t)
be the empirical process. It has been proved that ζ
n
, as n→∞ , converges to a deterministic measure-valued process which is the unique solution of a nonlinear differential equation.
In this paper we show that, under suitable conditions, ζ
n
converges to ζ at an exponential rate.
Accepted 20 October 1997 相似文献
3.
Mateusz B. Majka 《Stochastic Processes and their Applications》2017,127(12):4083-4125
We present a novel idea for a coupling of solutions of stochastic differential equations driven by Lévy noise, inspired by some results from the optimal transportation theory. Then we use this coupling to obtain exponential contractivity of the semigroups associated with these solutions with respect to an appropriately chosen Kantorovich distance. As a corollary, we obtain exponential convergence rates in the total variation and standard -Wasserstein distances. 相似文献
4.
Xing Huang 《随机分析与应用》2020,38(4):730-746
AbstractIn this paper, Wang’s Harnack inequalities and super Poincaré inequality for generalized Cox-Ingersoll-Ross model are obtained. Since the noise is degenerate, the intrinsic metric has been introduced to construct the coupling by change of measure. By using isoperimetric constant, some optimal estimate of the rate function in the super Poincaré inequality for the associated Dirichlet form is also obtained. 相似文献
5.
Tien Dung Nguyen 《Stochastic Processes and their Applications》2018,128(12):4154-4170
In this paper, based on techniques of Malliavin calculus, we obtain an explicit bound for tail probabilities of a general class of exponential functionals. We apply the obtained results to derive asymptotic behaviors for the tail of the exponential functional of stochastic differential equations. 相似文献
6.
《随机分析与应用》2013,31(3):515-543
We establish an exponential formula for the reachable sets of quantum stochastic differential inclusions (QSDI) which are locally Lipschitzian with convex values. Our main results partially rely on an auxilliary result concerning the density, in the topology of the locally convex space of solutions, of the set of trajectories whose matrix elements are continuously differentiable. By applying the exponential formula, we obtain results concerning convergence of the discrete approximations of the reachable set of the QSDI. This extends similar results of Wolenski[20] for classical differential inclusions to the present noncommutative quantum setting. 相似文献
7.
8.
9.
We extend the well posedness results for second order backward stochastic differential equations introduced by Soner, Touzi and Zhang (2012) [31] to the case of a bounded terminal condition and a generator with quadratic growth in the z variable. More precisely, we obtain uniqueness through a representation of the solution inspired by stochastic control theory, and we obtain two existence results using two different methods. In particular, we obtain the existence of the simplest purely quadratic 2BSDEs through the classical exponential change, which allows us to introduce a quasi-sure version of the entropic risk measure. As an application, we also study robust risk-sensitive control problems. Finally, we prove a Feynman–Kac formula and a probabilistic representation for fully non-linear PDEs in this setting. 相似文献
10.
《Quaestiones Mathematicae》2013,36(3):393-401
Abstract Dedicated to the memory of John Knopfmacher (1937–1999) We survey in this paper J. Knopfmacher results on number theoretical expansions as they arised from our common collaboration. 相似文献
11.
Abstract
In this paper, we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.
We show the squeezing property and the existence of finite dimensional exponential attractors for this equation
* The author is supported by the Postdoctoral Foundation of China 相似文献
12.
《Quaestiones Mathematicae》2013,36(4):399-408
Abstract Let A be a unitary Banach algebra and let B be a closed subalgebra of A that contains the unit. For an element of B we show in this note how both the singular and exponential spectrum depends on the algebra. 相似文献
13.
The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday. 相似文献
14.
Constrained diffusions, with diffusion matrix scaled by small ?>0, in a convex polyhedral cone G⊂Rk, are considered. Under suitable stability assumptions small noise asymptotic properties of invariant measures and exit times from domains are studied. Let B⊂G be a bounded domain. Under conditions, an “exponential leveling” property that says that, as ?→0, the moments of functionals of exit location from B, corresponding to distinct initial conditions, coalesce asymptotically at an exponential rate, is established. It is shown that, with appropriate conditions, difference of moments of a typical exit time functional with a sub-logarithmic growth, for distinct initial conditions in suitable compact subsets of B, is asymptotically bounded. Furthermore, as initial conditions approach 0 at a rate ?2 these moments are shown to asymptotically coalesce at an exponential rate. 相似文献
15.
We consider the spectrum of birth and death chains on an n-path. An iterative scheme is proposed to compute any eigenvalue with exponential convergence rate independent of n. This allows one to determine the whole spectrum in order n2 elementary operations. Using the same idea, we also provide a lower bound on the spectral gap, which is of the correct order on some classes of examples. 相似文献
16.
Bin Xie 《Journal of Differential Equations》2019,266(9):5254-5277
The hypercontractive property of the Markov semigroup associated with the reflected stochastic partial differential equation driven by the additive space–time white noise is mainly investigated. The main tool for its proof is the general criterion presented recently by F.-Y. Wang [29]. In particular, we obtain the hyperboundedness and the compactness of the Markov semigroup, the exponential convergences of the entropy, the exponential convergences of the Markov semigroup to its unique invariant measure in both and the total variation norm. 相似文献
17.
In this article, we partially solve a conjecture by Kochar and Korwar (1996) [9] in relation to the normalized spacings of the order statistics of a sample of independent exponential random variables with different scale parameters. In the case of a sample of size n=3, they proved the ordering of the normalized spacings and conjectured that result holds for all n. We prove this conjecture for n=4 for both spacings and normalized spacings and generalize some results to n>4. 相似文献
18.
J. S. Huang 《Annals of the Institute of Statistical Mathematics》1981,33(1):131-134
For two independent nonnegative random variablesX andY we say thatX is ageless relative toY if the conditional probability P[X> Y+x|X>Y] is defined and is equal to P[X>x] for allx>0. Suppose thatX is ageless relative to a nonlatticeY with P[Y=0]<P [Y<X]. We show that the only suchX is the exponential variable. As a corollary it follows that exponential variable is the only one which possesses the ageless
property relative to a continuous variable.
Research partially supported by NRC of Canada grants #A8057 and #T0500.
Work partially completed while on leave at Division of Math. Stat., C.S.I.R.O., Australia. 相似文献
19.
In this paper we study backward stochastic differential equations (BSDEs) driven by the compensated random measure associated to a given pure jump Markov process X on a general state space K. We apply these results to prove well-posedness of a class of nonlinear parabolic differential equations on K, that generalize the Kolmogorov equation of X. Finally we formulate and solve optimal control problems for Markov jump processes, relating the value function and the optimal control law to an appropriate BSDE that also allows to construct probabilistically the unique solution to the Hamilton–Jacobi–Bellman equation and to identify it with the value function. 相似文献
20.
In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf's is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936,Biometrika,28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly. 相似文献