共查询到10条相似文献,搜索用时 109 毫秒
1.
We study the filtering problem of an R
d
-valued pure jump process when the observations is a counting process. We assume that the dynamic of the state and the observations may be strongly dependent and that the two processes may jump together. Weak and pathwise uniqueness of solution of the Kushner–Stratonovich equation are discussed. 相似文献
2.
Markov chain approximations of reversible jump processes are investigated. Tightness results and a central limit theorem are
established. Moreover, given the generator of a reversible jump process with state space ℝ
d
, the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H
α/2(ℝ
d
), α∈(0,2), that is equivalent to the standard one.
相似文献
3.
A partially observable control problem for an R
d
-valued jump process with counting observations is studied. The state and the observations may be strongly dependent and, in particular, the two processes may jump together. An equivalent separated problem is introduced and the existence of an optimal control for the separated problem is obtained in the class of relaxed and generalized controls. Equivalence between the initial problem and the relaxed generalized separated control problem is discussed. 相似文献
4.
We consider state-dependent stochastic networks in the heavy-traffic diffusion limit represented by reflected jump-diffusions
in the orthant ℝ+
n
with state-dependent reflection directions upon hitting boundary faces. Jumps are allowed in each coordinate by means of
independent Poisson random measures with jump amplitudes depending on the state of the process immediately before each jump.
For this class of reflected jump-diffusion processes sufficient conditions for the existence of a product-form stationary
density and an ergodic characterization of the stationary distribution are provided. Moreover, such stationary density is
characterized in terms of semi-martingale local times at the boundaries and it is shown to be continuous and bounded. A central
role is played by a previously established semi-martingale local time representation of the regulator processes.
F.J. Piera’s research supported in part by CONICYT, Chile, FONDECYT Project 1070797.
R.R. Mazumdar’s research supported in part by NSF, USA, Grant 0087404 through Networking Research Program, and a Discovery
Grant from NSERC, Canada. 相似文献
5.
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
6.
Stephan Lawi 《Journal of Theoretical Probability》2008,21(1):144-168
We give a necessary and sufficient condition for a homogeneous Markov process taking values in ℝ
n
to enjoy the time-inversion property of degree α. The condition sets the shape for the semigroup densities of the process and allows to further extend the class of known
processes satisfying the time-inversion property. As an application we recover the result of Watanabe (Z. Wahrscheinlichkeitstheor.
Verwandte Geb. 31:115–124, 1975) for continuous and conservative Markov processes on ℝ+. As new examples we generalize Dunkl processes and construct a matrix-valued process with jumps related to the Wishart process
by a skew-product representation.
相似文献
7.
This paper establishes functional central limit theorems describing the heavy-traffic behavior of open single-class queueing networks with service interruptions. In particular, each station has a single server which is alternatively up and down. There are two treatments of the up and down times. The first treatment corresponds to fixed up and down times and leads to a reflected Brownian motion, just as when there are no service interruptions, but with different parameters. To represent long rare interruptions, the second treatment has growing up and down times with the up and down times being of ordern andn
1/2, respectively, when the traffic intensities are of order 1-n–1/2. In this case we establish convergence in the SkorohodM
1 topology to a multidimensional reflection of multidimensional Brownian motion plus a multidimensional jump process. 相似文献
8.
Atsushi Takeuchi 《随机分析与应用》2019,37(2):155-170
Consider real-valued processes determined by stochastic differential equations driven by Lévy processes. The jump parts of the driving Lévy process are not always α-stable ones, nor symmetric ones. In the present article, we shall study the pathwise uniqueness of the solutions to the stochastic differential equations under the conditions on the coefficients that the diffusion and the jump terms are Hölder continuous, while the drift one is monotonic. Our approach is based on Gronwall’s inequality. 相似文献
9.
Ricardo H. Nochetto Tobias von Petersdorff Chen-Song Zhang 《Numerische Mathematik》2010,116(3):519-552
We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order ${2s \in (0,2]}We consider elliptic and parabolic variational equations and inequalities governed by integro-differential operators of order
2s ? (0,2]{2s \in (0,2]}. Our main motivation is the pricing of European or American options under Lévy processes, in particular pure jump processes
or jump diffusion processes with tempered stable processes. The problem is discretized using piecewise linear finite elements
in space and the implicit Euler method in time. We construct a residual-type a posteriori error estimator which gives a computable
upper bound for the actual error in H
s
-norm. The estimator is localized in the sense that the residuals are restricted to the discrete non-contact region. Numerical
experiments illustrate the accuracy of the space and time estimators, and show that they can be used to measure local errors
and drive adaptive algorithms. 相似文献
10.
《随机分析与应用》2012,30(1):149-170
AbstractWe compute some functionals related to the generalized joint Laplace transforms of the first times at which two-dimensional jump processes exit half strips. It is assumed that the state space components are driven by Cox processes with both independent and common (positive) exponential jump components. The method of proof is based on the solutions of the equivalent partial integro-differential boundary-value problems for the associated value functions. The results are illustrated on several two-dimensional jump models of stochastic volatility which are based on non-affine analogs of certain mean-reverting or diverting diffusion processes representing closed-form solutions of the appropriate stochastic differential equations. 相似文献