共查询到20条相似文献,搜索用时 15 毫秒
1.
We give sufficient criteria for the Doléans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes, counting processes with stochastic intensities depending on diffusion processes as well as inhomogeneous finite-state Markov processes. 相似文献
2.
The main objective of this study is two-fold: First, we provide necessary and sufficient conditions for the positivity of Volterra integro-dynamical systems on time scales by means of Metzler matrices. Secondly, we show that positivity of the system implies uniform exponential stability of the trivial solution under sufficient conditions. 相似文献
3.
Gorica Pavlovi? Svetlana Jankovi? 《Applied mathematics and computation》2012,218(10):6125-6134
The main objective of the paper is to present sufficient conditions ensuring the pth mean and almost sure exponential stability, as well as the pth mean integrability of solutions to non-linear stochastic functional differential equations and, especially, to stochastic differential equations with time-varying lags. Some examples are given to illustrate the theoretical considerations. 相似文献
4.
Wenliang Huang 《Journal of Mathematical Analysis and Applications》2009,358(2):427-433
In this note we prove the exponential integrability of super-norms of general Itô's processes under certain assumptions, and then apply it to the diffusion processes determined by stochastic differential equations. In particular, a conjecture in [Y. Hu, Exponential integrability of diffusion processes, in: Contemp. Math., vol. 234, 1999, pp. 75-84] is solved. 相似文献
5.
Antonio Di Crescenzo Barbara Martinucci Nikita Ratanov 《Mathematical Methods in the Applied Sciences》2019,42(13):4606-4626
We consider the jump telegraph process when switching intensities depend on external shocks also accompanying with jumps. The incomplete financial market model based on this process is studied. The Esscher transform, which changes only unobservable parameters, is considered in detail. The financial market model based on this transform can price switching risks as well as jump risks of the model. 相似文献
6.
We consider the problem of minimum risk point estimation for the parameter =a+b of the exponential distribution with unknown location parameter and scale parameter when the loss function is squared error plus linear cost. In this paper, we propose a sequential estimator of and show that the associated risk is asymptotically one cost less than that given by Ghosh and Mukhopadhyay (1989,South African Statist. J.,23, 251–268). 相似文献
7.
This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the existence of Föllmer’s measure. This approach allows to extend well-known criteria of martingality from strictly positive to only nonnegative, continuous local martingales. 相似文献
8.
LIU PeiDe HOU YouLiang & WANG MaoFa School of Mathematics Statistics Wuhan University Wuhan China 《中国科学 数学(英文版)》2010,(4)
In this paper,the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are discussed.In particular,a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established;the relationships between these spaces are investigated.Moreover,the boundedness of several sublinear operators from one weak Orlicz space to another is proved;their vector-valued analogues are also considered. 相似文献
9.
YAN Jun 《高校应用数学学报(英文版)》2015,(2):210-216
In this article, we construct an exponential martingale for the compound Poisson process with latent variableWith the help of this exponential martingale, we provide an asymptotic behavior of the coherent entropic risk measure for the compound Poisson process and a deviation inequality for the ruin probability of the partly shifted risk process. 相似文献
10.
Maryam Tahmasebi Gholam Hossein Yari 《Stochastics An International Journal of Probability and Stochastic Processes》2020,92(4):595-612
In this paper, we focused on computing the minimal relative entropy between the original probability and all of the equivalent martin gale measure for the Lévy process. For this purpose, the quasiMonte Carlo method is used. The probability with minimal relative entropy has many suitable properties. This probability has the minimal Kullback-Leibler distance to the original probability. Also, by using the minimal relative entropy the exponential utility indifference price can be found. In this paper, the Monte Carlo and quasi-Monte Carlo methods have been applied. In the quasi-Monte Carlo method, two types of widely used lowdiscrepancy sequences, Halton sequence and Sobol sequence, are used. These methods have been used for exponential Lévy process such as variance gamma and CGMY process. In these two processes, the minimal relative entropy has been computed by Monte Carlo and quasi-Monte Carlo, and compared their results. The results show that quasi-Monte Carlo with Sobol sequence performs better in terms of fast convergence and less error. Finally, this method by fitting the variance gamma model and parameters estimation for the model has been implemented for financial data and the corresponding minimal relative entropy has been computed. 相似文献
11.
We prove that the linear switching system , where is bounded valued square matrices and ?:[0,1,2,…)→Ω is an arbitrary switching signals, is uniformly exponentially stable if the sequence is bounded, where s(k) is bounded valued sequence. 相似文献
12.
Banach空间值鞅变换的有界性及其应用 总被引:7,自引:0,他引:7
本文给出关于Banach空间值鞅变换算子有界性的一种新的处理方法,得到一系列带有广泛性的结果,并应用鞅变换算子的有界性刻画了Banach空间的一致光滑性和一致凸性,使得许多已有文献中的结论成为本文的特例. 相似文献
13.
In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I* and Cesàro mean operator σ* are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα (0 < α < ∞), respectively. The facts show that it depends on the geometrical properties of the Banach space. 相似文献
14.
We study the connection between the martingale and free-boundary approaches in sequential detection problems for the drift of a Brownian motion, under the assumption of exponential penalty for the delay. By means of the solution of a suitable free-boundary problem, we show that the reward process can be decomposed into the product between a gain function of the boundary point and a positive martingale inside the continuation region. 相似文献
15.
Trevor J. Sweeting 《Statistics & probability letters》1983,1(3):115-119
It is shown that, by suitable random normalisation, the spacings (differences between order statistics) of exponential and uniform samples are independent. These normalised spacings can be used for consecutive discordancy testing when scale (and possibly also location) parameters are unknown. 相似文献
16.
Keigo Yamada 《Stochastic Processes and their Applications》1985,19(1):101-109
We consider a storage process with finite or infinite capacity having a compound Poisson process as input and general release rule. For this process we derive some exponential type upper and lower bounds for hitting time distributions by means of martingale theory. 相似文献
17.
Coenraad C.A. Labuschagne Valeria Marraffa 《Journal of Mathematical Analysis and Applications》2010,363(2):357-365
We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon-Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney-Schaefer l-tensor product , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon-Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on . Secondly, we derive a Riesz decomposition for uniform amarts of maps acting between a Banach lattice and a Banach space. This result is used to characterize Banach spaces with the Radon-Nikodým property in terms of uniformly norm bounded uniform amarts of maps that are norm convergent. In the case 1<p<∞, our results yield Lp(μ,Y)-space analogues of some of the well-known results on uniform amarts in L1(μ,Y)-spaces. 相似文献
18.
引入了原子鞅与正则原子鞅概念、并研究了两类Banach空间值鞅Hardy空间的原子分解和有限鞅的稠密性,所得结论揭示了鞅Hardy空间正则原子鞅分解的存在性,有限鞅的稠密性和Banach空间的一致光滑性(或一致凸性)三者之间的内在联系. 相似文献
19.
We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant ellipse.More precisely,a quadratic system having an invariant ellipse can be written into the form x=x2+y2-1+y(ax+by+c),y=x(ax+by+c),and the ellipse becomes x2+y2=1.We prove that(i) this quadratic system is analytic integrable if and only if a=0;(ii) if x2+y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2+y2=1 is not a limit cycle;and(iii) if x2+y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0. 相似文献
20.
Paul Sablonnire 《Journal of Computational and Applied Mathematics》2008,219(2):509-517
This paper is the continuation of a work initiated in [P. Sablonnière, An algorithm for the computation of Hermite–Padé approximations to the exponential function: divided differences and Hermite–Padé forms. Numer. Algorithms 33 (2003) 443–452] about the computation of Hermite–Padé forms (HPF) and associated Hermite–Padé approximants (HPA) to the exponential function. We present an alternative algorithm for their computation, based on the representation of HPF in terms of integral remainders with B-splines as Peano kernels. Using the good properties of discrete B-splines, this algorithm gives rise to a great variety of representations of HPF of higher orders in terms of HPF of lower orders, and in particular of classical Padé forms. We give some examples illustrating this algorithm, in particular, another way of constructing quadratic HPF already described by different authors. Finally, we briefly study a family of cubic HPF. 相似文献