共查询到20条相似文献,搜索用时 140 毫秒
1.
We consider optimal control problems for one-dimensional diffusion processes [ILM0001] where the control processes υt are increasing, positive, and adapted. Several types of expected cost structures associated with each policy υ(.) are adopted, e.g. discounted cost, long term average cost and time average cost. Our work is related to [2,6,12,14,16 and 21], where diffusions are allowed to evolve in the whole space, and to [13] and [20], where diffusions evolve only in bounded regions. We shall present some analytic results about value functions, mainly their characterizations, by simple dynamic programming arguments. Several simple examples are explicitly solved to illustrate the singular behaviour of our problems. 相似文献
2.
Stephanos Venakides 《纯数学与应用数学通讯》1985,38(2):125-155
The inverse scattering method is used to determine the distribution limit as ? → 0 of the solution u(x, t, ?) of the initial value problem. Ut ? 6uux + ?2uxxx = 0, u(x, 0) = v(x), where v(x) is a positive bump which decays sufficiently fast as x x→±α. The case v(x) ? 0 has been solved by Peter D. Lax and C. David Levermore [8], [9], [10]. The computation of the distribution limit of u(x, t, ?) as ? → 0 is reduced to a quadratic maximization problem, which is then solved. 相似文献
3.
Prof. Moshe Zakai 《Probability Theory and Related Fields》1969,11(3):230-243
Summary Let x(t) be a diffusion process satisfying a stochastic differential equation and let the observed process y(t) be related to x(t) by dy(t) = g(x(t)) + dw(t) where w(t) is a Brownian motion. The problem considered is that of finding the conditional probability of x(t) conditioned on the observed path y(s), 0st. Results on the Radon-Nikodym derivative of measures induced by diffusions processes are applied to derive equations which determine the required conditional probabilities. 相似文献
4.
Markov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x ? X, y ? Y, t ? 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x<y} is established for one-dimensional diffusions, and several new results on entrance and exit laws for diffusions, birth-death processes, and discrete time birth-death chains are obtained. 相似文献
5.
Let x t be a diffusion process observed via a noisy sensor, whose output is yt We consider the problem of evaluating the maximum a posteriori trajectory {xs0≤ s ≤ t Based on results of Stratonovich [1] and Ikeda-Watanabe [2], we show that this estimator is given by the solution of an appropriate variational problem which is a slight modification of the "minimum energy" estimator. We compare our results to the non-linear filtering theory and show that for problems which possess a finite dimensional solution, our approach yields also explicit filters. For linear diffusions observed via linear sensors, these filters are identical to the Kalman-filter 相似文献
6.
S. Haruki 《Aequationes Mathematicae》2002,63(3):201-209
Summary. Let (G, +) and (H, +) be abelian groups such that the equation 2u = v 2u = v is solvable in both G and H. It is shown that if f1, f2, f3, f4, : G ×G ? H f_1, f_2, f_3, f_4, : G \times G \longrightarrow H satisfy the functional equation f1(x + t, y + s) + f2(x - t, y - s) = f3(x + s, y - t) + f4(x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , then f1, f2, f3, and f4 are given by f1 = w + h, f2 = w - h, f3 = w + k, f4 = w - k where w : G ×G ? H w : G \times G \longrightarrow H is an arbitrary solution of f (x + t, y + s) + f (x - t, y - s) = f (x + s, y - t) + f (x - s, y + t) for all x, y, s, t ? G x, y, s, t \in G , and h, k : G ×G ? H h, k : G \times G \longrightarrow H are arbitrary solutions of Dy,t3g(x,y) = 0 \Delta_{y,t}^{3}g(x,y) = 0 and Dx,t3g(x,y) = 0 \Delta_{x,t}^{3}g(x,y) = 0 for all x, y, s, t ? G x, y, s, t \in G . 相似文献
7.
The following system considered in this paper:
x¢ = - e(t)x + f(t)fp*(y), y¢ = - (p-1)g(t)fp(x) - (p-1)h(t)y,x' = -\,e(t)x + f(t)\phi_{p^*}(y), \qquad y'= -\,(p-1)g(t)\phi_p(x) - (p-1)h(t)y, 相似文献
8.
We consider a diffusion process {x(t)} on a compact Riemannian manifold with generator δ/2 + b. A current‐valued continuous stochastic process {X t} in the sense of Itô [8] corresponds to {x(t)} by considering the stochastic line integral X t(a) along {x(t)} for every smooth 1-form a. Furthermore {X t} is decomposed into the martingale part and the bounded variation part as a current-valued continuous process. We show the central limit theorems for {X t} and the martingale part of {X t}. Occupation time laws for recurrent diffusions and homogenization problems of periodic diffusions are closely related to these theorems 相似文献
9.
The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function \documentclass{article}\pagestyle{empty}\begin{document}$ \Theta (x,t) = \upsilon *(x,t;0) + 2\sum\limits_{n = 1}^\infty {v*(x,t;y_n)} $\end{document} for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function. 相似文献
10.
We consider an Abel equation (*)y’=p(x)y
2 +q(x)y
3 withp(x), q(x) polynomials inx. A center condition for (*) (closely related to the classical center condition for polynomial vector fields on the plane)
is thaty
0=y(0)≡y(1) for any solutiony(x) of (*).
Folowing [7], we consider a parametric version of this condition: an equation (**)y’=p(x)y
2 +εq(x)y
3
p, q as above, ε ∈ ℂ, is said to have a parametric center, if for any ɛ and for any solutiony(ɛ,x) of (**)y(ɛ, 0)≡y(ɛ, 1)..
We give another proof of the fact, shown in [6], that the parametric center condition implies vanishing of all the momentsm
k
(1), wherem
k
(x)=∫
0
x
pk
(t)q(t)(dt),P(x)=∫
0
x
p(t)dt. We investigate the structure of zeroes ofm
k
(x) and generalize a “canonical representation” ofm
k
(x) given in [7]. On this base we prove in some additional cases a composition conjecture, stated in [6, 7] for a parametric
center problem.
The research of the first and the third author was supported by the Israel Science Foundation, Grant No. 101/95-1 and by the
Minerva Foundation. 相似文献
11.
Shuguan Ji 《Calculus of Variations and Partial Differential Equations》2008,32(2):137-153
In this paper, we study the problem of time periodic solutions to the nonlinear wave equation with x-dependent coefficients on under the boundary conditions a
1
y(0, t)+b
1
y
x
(0, t) = 0, ( for i = 1, 2) and the periodic conditions y(x, t + T) = y(x, t), y
t
(x, t + T) = y
t
(x, t). Such a model arises from the forced vibrations of a bounded nonhomogeneous string and the propagation of seismic waves
in nonisotropic media. For , we establish the existence of time periodic solutions in the weak sense by utilizing some important properties of the wave
operator with x-dependent coefficients.
This work was supported by the 985 Project of Jilin University, the Specialized Research Fund for the Doctoral Program of
Higher Education, and the Science Research Foundation for Excellent Young Teachers of College of Mathematics at Jilin University. 相似文献
12.
This paper deals with a class of localized and degenerate quasilinear parabolic systems
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