共查询到20条相似文献,搜索用时 15 毫秒
1.
Yangrong Li 《Journal of Mathematical Analysis and Applications》2006,313(2):461-474
In this paper, we investigate duality and Feller-Reuter-Riley (FRR) property of continuous-time Markov chains (CTMCs). A criterion of dual q-functions is given in terms of their q-matrices. For a dual q-matrix Q, a necessary and sufficient conditions for the minimal Q-function to be a FRR transition function are also given. Finally, by using dual technique, we give a criterion of FRR Q-functions when Q is monotone. 相似文献
2.
Eugene A. Feinberg Manasa Mandava Albert N. Shiryaev 《Journal of Mathematical Analysis and Applications》2014
This paper studies three ways to construct a nonhomogeneous jump Markov process: (i) via a compensator of the random measure of a multivariate point process, (ii) as a minimal solution of the backward Kolmogorov equation, and (iii) as a minimal solution of the forward Kolmogorov equation. The main conclusion of this paper is that, for a given measurable transition intensity, commonly called a Q-function, all these constructions define the same transition function. If this transition function is regular, that is, the probability of accumulation of jumps is zero, then this transition function is the unique solution of the backward and forward Kolmogorov equations. For continuous Q-functions, Kolmogorov equations were studied in Feller?s seminal paper. In particular, this paper extends Feller?s results for continuous Q-functions to measurable Q-functions and provides additional results. 相似文献
3.
Pan ZHAO 《数学学报(英文版)》2018,(9)
For the continuous time Markov chain with transition function P(t) on Z_+~d, we give the necessary and sufficient conditions for the existence of its Siegmund dual with transition function P(t).If Q, the q-matrix of P(t), is uniformly bounded, we show that the Siegmund dual relation can be expressed directly in terms of q-matrices, and a sufficient condition under which the Q-function is the Siegmund dual of some Q-function is also given. 相似文献
4.
Joris Bierkens 《Journal of Mathematical Analysis and Applications》2011,379(2):469-481
The strong Feller property is an important quality of Markov semigroups which helps for example in establishing uniqueness of invariant measure. Unfortunately degenerate stochastic evolutions, such as stochastic delay equations, do not possess this property. However the eventual strong Feller property is sufficient in establishing uniqueness of invariant probability measure. In this paper we provide operator theoretic conditions under which a stochastic evolution equation with additive noise possesses the eventual strong Feller property. The results are used to establish uniqueness of invariant probability measure for stochastic delay equations and stochastic partial differential equations with delay, with an application in neural networks. 相似文献
5.
首先, 当$Q$是一个拟单调的q矩阵的时候,
我们找出最小的$Q$函数是一个Feller的转移函数的准则.
然后我们把这个结论应用于生成分支q矩阵并得到相应的生成分支过程的Feller准则.
特别地, 设$\theta$是分支q矩阵中的非线性数,
总是存在一个分点$\theta_0$满足$1\leq\theta_0\leq2$或$\theta_0<+\infty$使得
生成分支过程是否是Feller的要依据$\theta<\theta_0$或者$\theta>\theta_0$. 相似文献
6.
7.
Dirk Veestraeten 《Integral Transforms and Special Functions》2020,31(5):368-382
ABSTRACTThe Laplace transforms of the transition probability density and distribution functions of the Feller process contain products of a Kummer and a Tricomi confluent hypergeometric function. The intricacies caused by the singularity at 0 of the Feller process imply that ultimately seven new inverse Laplace transforms can be derived of which four contain the Marcum Q function. The results of this paper together with a scarcely used link between the Marcum and Nuttall Q functions also provide two alternative proofs for an existing identity involving two Marcum Q functions with reversed arguments. The paper also expands the existing expression for the Marcum Q function with identical arguments and order 1. In particular, the new formula applies to all integer and fractional values of the order and is expressed in terms of the generalized hypergeometric function. 相似文献
8.
Rögnvaldur Ingthorsson 《Metaphysica》2008,9(2):129-137
According to the truth-functional analysis of conditions, to be ‘necessary for’ and ‘sufficient for’ are converse relations. From this, it follows that to be ‘necessary and sufficient for’ is a symmetric relation, that is, that if P is a necessary and sufficient condition for Q, then Q is a necessary and sufficient condition for P. This view is contrary to common sense. In this paper, I point out that it is also contrary to a widely accepted ontological view of conditions, according to which if P is a necessary and sufficient condition for Q, then Q is in no sense a condition for P; it is a mere consequence of P. 相似文献
9.
《Stochastic Processes and their Applications》2020,130(5):2693-2736
We give necessary and sufficient criteria for the Feller–Dynkin property of solutions to martingale problems in terms of Lyapunov functions. Moreover, we derive a Khasminskii-type integral test for the Feller–Dynkin property of multidimensional diffusions with random switching. For one dimensional switching diffusions with state-independent switching, we provide an integral-test for the Feller–Dynkin property. 相似文献
10.
Yangrong Li 《Journal of Mathematical Analysis and Applications》2007,328(1):640-654
A column continuous transition function is by definition a standard transition function P(t) whose every column is continuous for t?0 in the norm topology of bounded sequence space l∞. We will prove that it has a stable q-matrix and that there exists a one-to-one relationship between column continuous transition functions and increasing integrated semigroups on l∞. Using the theory of integrated semigroups, we give some necessary and sufficient conditions under which the minimal q-function is column continuous, in terms of its generator (of the Markov semigroup) as well as its q-matrix. Furthermore, we will construct all column continuous Q-functions for a conservative, single-exit and column bounded q-matrix Q. As applications, we find that many interesting continuous-time Markov chains (CTMCs), say Feller-Reuter-Riley processes, monotone processes, birth-death processes and branching processes, etc., have column continuity. 相似文献
11.
Jian Wang 《Integral Equations and Operator Theory》2013,76(2):151-161
We present a sufficient condition for fractional Laplacian with gradient perturbation to generate a sub-Markovian C 0-semigroup on ${L^1(\mathbb{R}^d, dx)}$ . The condition also yields the ultracontractivity of the semigroup and an upper on-diagonal estimate of the associated transition kernel. Based on the subordination technique, the extension to general pure jump Lévy process with gradient perturbation is studied. As a direct application, we obtain sufficient conditions for the strong Feller property of stochastic differential equations driven by additive Lévy process. 相似文献
12.
Toshihiko Yamada 《Journal of Number Theory》1973,5(3):179-190
Let k be a real quadratic field, and a central division quaternion algebra over k. In this paper sufficient conditions are given to insure that appears in a simple component of the group algebra Q[G] of some finite group G over the rational field Q. In particular, when k is assumed to be Q(√2) or Q(√5), the necessary and sufficient conditions for to appear in some Q[G] are given. 相似文献
13.
14.
A Markov integrated semigroup G(t) is by definition a weaklystar differentiable and increasing contraction integrated semigroup on l
∞. We obtain a generation theorem for such semigroups and find that they are not integrated C
0-semigroups unless the generators are bounded. To link up with the continuous-time Markov chains (CTMCs), we show that there
exists a one-to-one relationship between Markov integrated semigroups and transition functions. This gives a clear probability
explanation of G(t): it is just the mean transition time, and allows us to define and to investigate its q-matrix. For a given q-matrix Q, we give a criterion for the minimal Q-function to be a Feller-Reuter-Riley (FRR) transition function, this criterion gives an answer to a long-time question raised
by Reuter and Riley (1972).
This research was supported by the China Postdoctoral Science Foundation (No.2005038326). 相似文献
15.
16.
Normal cone and subdifferential have been generalized through various continuous functions; in this article, we focus on a non separable Q-subdifferential version. Necessary and sufficient optimality conditions for unconstrained nonconvex problems are revisited accordingly. For inequality constrained problems, Q-subdifferential and the lagrangian multipliers, enhanced as continuous functions instead of scalars, allow us to derive new necessary and sufficient optimality conditions. In the same way, the Legendre-Fenchel conjugate is generalized into Q-conjugate and global optimality conditions are derived by Q-conjugate as well, leading to a tighter inequality. 相似文献
17.
Branko Ćurgus Andreas Fleige Aleksey Kostenko 《Integral Equations and Operator Theory》2013,77(4):533-557
We consider a regular indefinite Sturm–Liouville eigenvalue problem ?f′′ + q f = λ r f on [a, b] subject to general self-adjoint boundary conditions and with a weight function r which changes its sign at finitely many, so-called turning points. We give sufficient and in some cases necessary and sufficient conditions for the Riesz basis property of this eigenvalue problem. In the case of separated boundary conditions we extend the class of weight functions r for which the Riesz basis property can be completely characterized in terms of the local behavior of r in a neighborhood of the turning points. We identify a class of non-separated boundary conditions for which, in addition to the local behavior of r in a neighborhood of the turning points, local conditions on r near the boundary are needed for the Riesz basis property. As an application, it is shown that the Riesz basis property for the periodic boundary conditions is closely related to a regular HELP-type inequality without boundary conditions. 相似文献
18.
A necessary and sufficient condition for a Hermitian operator on a Hilbert space to be expressed as aP + bQ with some projections P, Q and reals a, b is established. Moreover the spectrum of such an operator is explicitly drawn in terms of the spectrum of PQ ∣ran P, the restriction to the range of P. 相似文献
19.
Contraction Integrated Semigroups and Their Application to Continuous-time Markov Chains 总被引:11,自引:0,他引:11
YangRongLI 《数学学报(英文版)》2003,19(3):605-618
We introduce the notion of the contraction integrated semigroups and give the Lumer-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix. 相似文献
20.
For a linear boundary value problem for a Fredholm integro-differential equation, we obtain necessary and sufficient conditions for the unique solvability in terms of a matrix Q ν m (h) formed on the basis of the matrices of boundary conditions, the differential part, the integral term, and a partition with increment h > 0 of the interval on which the problem is defined. 相似文献