共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we extend Walsh’s stochastic integral with respect to a Gaussian noise, white in time and with some homogeneous
spatial correlation, in order to be able to integrate some random measure-valued processes. This extension turns out to be
equivalent to Dalang’s one. Then we study existence and regularity of the density of the probability law for the real-valued
mild solution to a general second order stochastic partial differential equation driven by such a noise. For this, we apply
the techniques of the Malliavin calculus. Our results apply to the case of the stochastic heat equation in any space dimension
and the stochastic wave equation in space dimension d=1,2,3. Moreover, for these particular examples, known results in the literature have been improved.
相似文献
2.
We study the optimal control for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend
on the state of the solution process as well as of its expected value. Moreover, the cost functional is also of mean-field
type. This makes the control problem time inconsistent in the sense that the Bellman optimality principle does not hold. For
a general action space a Peng’s-type stochastic maximum principle (Peng, S.: SIAM J. Control Optim. 2(4), 966–979, 1990) is derived, specifying the necessary conditions for optimality. This maximum principle differs from the classical one in
the sense that here the first order adjoint equation turns out to be a linear mean-field backward SDE, while the second order
adjoint equation remains the same as in Peng’s stochastic maximum principle. 相似文献
3.
The generalized Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman’s urn model with both homogeneous and non-homogeneous generating matrices.The Gaussian process is a solution of ... 相似文献
4.
A stochastic variational inequality is proposed to model a white noise excited elasto-plastic oscillator. The solution of
this inequality is essentially a continuous diffusion process for which a governing diffusion equation is obtained to study
the evolution in time of its probability distribution. The diffusion equation is degenerate, but using the fact that the degeneracy
occurs on a bounded region we are able to show the existence of a unique solution satisfying the desired properties. We prove
the ergodic properties of the process and characterize the invariant measure. Our approach relies on extending Khasminskii’s
method (Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1980), which in the present context leads to the study of degenerate Dirichlet problems with nonlocal boundary conditions.
This research was partially supported by a grant from CEA, Commissariat à l’énergie atomique and by the National Science Foundation
under grant DMS-0705247. 相似文献
5.
I. A. Soloviev 《Theoretical and Mathematical Physics》1997,111(3):676-685
We suggest a theory of stochastic waves that describe the behavior of random vectors satisfying a set of ordinary first-order
differential equations. The equation for the stochastic waves is given for the case where the mean values are described by
a differential model. The relationship between this equation and the Liouville equation is considered and analogue of the
Ehrenfest theorem is proved. For the covariance of a component of a random vector, we obtain an ordinary first-order differential
equation. Interpretation of Planck’s constant is discussed. Conditions are formulated under which wave packets propagate with
increasing or decreasing covariance.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 356–368, June, 1997. 相似文献
6.
We find sufficient conditions for the coefficients of a diffusion equation on a noncompact manifold that guarantee the nonexplosion
of solutions in finite time. This property leads to the existence and uniqueness of solutions for the corresponding stochastic
differential equation with globally non-Lipschitz coefficients.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1454–1472, November, 2007. 相似文献
7.
The aim of this paper is to investigate the convergence properties for Mordukhovich’s coderivative of the solution map of
the sample average approximation (SAA) problem for a parametric stochastic generalized equation. It is demonstrated that,
under suitable conditions, both the cosmic deviation and the ρ-deviation between the coderivative of the solution mapping to SAA problem and that of the solution mapping to the parametric
stochastic generalized equation converge almost surely to zero as the sample size tends to infinity. Moreover, the exponential
convergence rate of coderivatives of the solution maps to the SAA parametric generalized equations is established. The results
are used to develop sufficient conditions for the consistency of the Lipschitz-like property of the solution map of SAA problem
and the consistency of stationary points of the SAA estimator for a stochastic mathematical program with complementarity constraints. 相似文献
8.
The problem of counting ramified covers of a Riemann surface up to homeomorphism was proposed by Hurwitz in the late 1800’s.
This problem translates combinatorially into factoring a permutation of specified cycle type, with certain conditions on the
cycle types of the factors, such as minimality and transitivity.
Goulden and Jackson have given a proof for the number of minimal, transitive factorizations of a permutation into transpositions.
This proof involves a partial differential equation for the generating series, called the Join-Cut equation. Recently, Bousquet-Mélou
and Schaeffer have found the number of minimal, transitive factorizations of a permutation into arbitrary unspecified factors.
This was proved by a purely combinatorial argument, based on a direct bijection between factorizations and certain objects
called m-Eulerian trees.
In this paper, we give a simple partial differential equation for Bousquet-Mélou and Schaeffer’s generating series, and for
Goulden and Jackson’s generating series, as well as a new proof of the result by Bousquet-Mélou and Schaeffer. We apply algebraic
methods based on Lagrange’s theorem, and combinatorial methods based on a new use of Bousquet-Mélou and Schaeffer’s m-Eulerian trees.
Supported by a Discovery Grant from NSERC.
Research supported by a Postgraduate Scholarship from NSERC.
Received October 8, 2005 相似文献
9.
Raphael Kruse 《BIT Numerical Mathematics》2012,52(1):109-140
The focus of this article lies on the bistability of multistep methods applied to stochastic ordinary differential equations.
Here bistability is understood in the sense of F. Stummel and leads to two-sided estimates of the strong error of convergence.
It is shown that bistability can be characterized by Dahlquist’s strong root condition. The main ingredient of the stability
analysis is a stochastic version of Spijker’s norm. 相似文献
10.
A Property of <Emphasis Type="Italic">g</Emphasis>-Expectation 总被引:6,自引:0,他引:6
LongJIANG 《数学学报(英文版)》2004,20(5):769-778
This paper proves that, under the hypothesis g(t, 0, 0) ≡ 0 and some natural assumptions, the generator g of a backward stochastic differential equation can be uniquely determined by the corresponding g-expectations with all terminal conditions. The main result of this paper also confirms and extends Peng Shige‘s conjecture. 相似文献
11.
Kennaugh’s pseudo-eigenvalue equation is a basic equation that plays an extremely important role in radar polarimetry. In
this paper, by means of real representation, we first present a necessary and sufficient condition for the general Kennaugh’s
pseudo-eigenvalue equation having a solution, characterize the explicit form of the solution, and then study the solution
of Kennaugh’s pseudo-eigenvalue equation. At last, we propose a new technique for finding the coneigenvalues and coneigenvectors
of a complex matrix under appropriate conditions in radar polarimetry. 相似文献
12.
V. V. Karachik 《Computational Mathematics and Mathematical Physics》2011,51(9):1567-1587
A polynomial solution of the inhomogeneous Dirichlet problem for Poisson’s equation with a polynomial right-hand side is found.
An explicit representation of the harmonic functions in the Almansi formula is used. The solvability of a generalized third
boundary value problem for Poisson’s equation is studied in the case when the value of a polynomial in normal derivatives
is given on the boundary. A polynomial solution of the third boundary value problem for Poisson’s equation with polynomial
data is found. 相似文献
13.
Nonholonomic systems are described by the Lagrange-D’Alembert’s principle. The presence of symmetry leads, upon the choice
of an arbitrary principal connection, to a reduced D’Alembert’s principle and to the Lagrange-D’Alembert-Poincaré reduced
equations. The case of rolling constraints has a long history and it has been the purpose of many works in recent times. In
this paper we find reduced equations for the case of a thick disk rolling on a rough surface, sometimes called Euler’s disk, using a 3-dimensional abelian group of symmetry. We also show how the reduced system can be transformed into a single second
order equation, which is an hypergeometric equation. 相似文献
14.
T. Androshchuk 《Journal of Mathematical Sciences》2007,147(4):6847-6863
We consider the Unit Root Bilinear model with a sequence of innovations given by a fractional Gaussian noise (increases of
a fractional Brownian motion). For such a model, we prove a variant of the Donsker-Prokhorov limit theorem and establish the
convergence of the model in probability to a solution of a proper stochastic differential equation with FBM. The proof is
based on a result on convergence of the Euler’s scheme with “small perturbations” for SDE with FBM, which is also proved.
Bibliography: 20 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 5–33. 相似文献
15.
Jörn Sass 《Acta Appl Math》2007,97(1-3):221-238
We consider a market model where stock returns satisfy a stochastic differential equation with an unobservable, stochastic
drift process. The investor’s objective is to maximize expected utility of terminal wealth, but investment decisions are based
on the knowledge of the stock prices only. The performance of the resulting highly risky strategies can be improved considerably
by imposing convex constraints covering e.g. short selling restrictions. Using filtering methods we transform the model to
a model with full information. We provide a verification result and show how results on optimization under convex constraints
can be used directly for a continuous time Markov chain model for the drift. In special cases we derive representations of
the optimal trading strategies, including a stochastic volatility model.
Supported by the Austrian Science Fund, FWF grant P17947-N12. 相似文献
16.
Jin-zhi Li 《应用数学学报(英文版)》2009,25(2):345-352
We consider an infinite capacity second-order fluid queue with subordinator input and Markovmodulated linear release rate. The fluid queue level is described by a generalized Langevin stochastic differential equation (SDE). Applying infinitesimal generator, we obtain the stationary distribution that satisfies an integro-differential equation. We derive the solution of the SDE and study the transient level's convergence in distribution. When the coefficients of the SDE are constants, we deduce the system transient property. 相似文献
17.
The communication mix is a relevant decision issue for an organization that plans the advertising campaign for a fixed future event. It is assumed that the objectives of the organization are to minimize the cost of the advertising campaign and to drive the final demand as close as possible to a target value. Two different advertising channels are available: the first affects deterministically the consumers’ demand, whereas the second presents some stochastic aspects which are out of decision-maker’s control. Some recent mathematical developments on the stochastic linear quadratic control problem allow to formulate and solve some interesting instances of the problem. A comparative analysis of the efficiency of deterministic and stochastic controls is done and the optimal feedback policies are discussed. The trade-off between efficiency and risk of an advertising channel is essential to understand the features of the optimal solutions.This study was supported by MIUR and University of Padua. 相似文献
18.
E. V. Dulov 《Journal of Applied Mathematics and Computing》2000,7(1):41-60
In this paper we consider a series of algorithms for calculating radicals of matrix polynomial equations. A particular aspect of this problem arise in author’s work, concerning parameter identification of linear dynamic stochastic system. Special attention is given to searching the solution of an equation in a neighbourhood of some initial approximation. The offered approaches and algorithms allow us to receive fast and quite exact solution. We give some recommendations for application of given algorithms. 相似文献
19.
John Kornak Mark E. Irwin Noel Cressie 《Statistical Inference for Stochastic Processes》2006,9(1):31-46
The study of stochastic processes can take many forms. Theoretical properties are important to ensure consistent model definition.
Statistical inference on unknown parameters is equally important but can be difficult. This is principally because many of
the standard assumptions for proving consistency and asymptotic normality of estimators involve independence and homogeneity.
In the case where inference is concerned with detecting change in a spatial process from one time point to another, a statistical-computing
approach can be rewarding. Regardless of the complexity of the stochastic process, if simulating from it is relatively easy,
then detecting change is possible using a Monte Carlo approach. The methodology is applied in a military scenario, where a
country’s defensive posture changes as a function of its perceived threat. For tactical-decision purposes, it is extremely
important to know whether the country’s perceived threat level has changed. 相似文献
20.
Holger Drees 《Extremes》2008,11(1):35-53
On the occasion of Laurens de Haan’s 70th birthday, we discuss two aspects of the statistical inference on the extreme value
behavior of time series with a particular emphasis on his important contributions. First, the performance of a direct marginal
tail analysis is compared with that of a model-based approach using an analysis of residuals. Second, the importance of the
extremal index as a measure of the serial extremal dependence is discussed by the example of solutions of a stochastic recurrence
equation.
相似文献