共查询到20条相似文献,搜索用时 15 毫秒
1.
Shige Peng 《Applied Mathematics and Optimization》1993,27(2):125-144
We study the existence and uniqueness of the following kind of backward stochastic differential equation, $$x(t) + \int_t^T {f(x(s),y(s),s)ds + \int_t^T {y(s)dW(s) = X,} }$$ under local Lipschitz condition, where (Ω, ?,P, W(·), ?t) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ?t-adapted process, andX is ?t-measurable. The problem is to look for an adapted pair (x(·),y(·)) that solves the above equation. A generalized matrix Riccati equation of that type is also investigated. A new form of stochastic maximum principle is obtained. 相似文献
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The fractional stochastic differential equations have wide applications in various fields of science and engineering. This paper addresses the issue of existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces. Using fractional calculations, fixed point technique, stochastic analysis theory and methods adopted directly from deterministic fractional equations, new set of sufficient conditions are formulated and proved for the existence of mild solutions for the fractional impulsive stochastic differential equation with infinite delay. Further, we study the existence of solutions for fractional stochastic semilinear differential equations with nonlocal conditions. Examples are provided to illustrate the obtained theory. 相似文献
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Paul H. Bezandry 《Applicable analysis》2013,92(7):819-827
The article introduces and studies the concept of p-mean almost periodicity for stochastic processes. Our abstract results are, subsequently, applied to studying the existence of square-mean almost periodic solutions to some semilinear stochastic equations. 相似文献
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Leszek Słomiński 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(5):275-293
The problem of approximation of a solution to a reflecting stochastic differential equation (SDE) with jumps by a sequence of solutions to SDEs with penalization terms is considered. The approximating sequence is not relatively compact in the Skorokhod topology J 1 and so the methods of approximation based on the J 1-topology break down. In the paper, we prove our convergence results in the S-topology on the Skorokhod space D(R+,?R d ) introduced recently by Jakubowski. The S-topology is weaker than J 1 but stronger than the Meyer-Zheng topology and shares many useful properties with J 1. 相似文献
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The standard existence and uniqueness theorem for stochastic differential equations requires Lipschitz condition of the coefficients. In this paper, we extend these results to the case in which the coefficients are not required to be Lipschitz continuous, instead they only satisfy a ‘weak’ type of Lipschitz condition. 相似文献
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This paper investigates the existence and uniqueness theorem of solutions to neutral stochastic differential equations with infinite delay (short for INSFDEs) at a space BC((-∞,0];Rd). Under the uniform Lipschitz condition, linear growth condition is weaken to obtain the moment estimate of the solution for INSFDEs. Furthermore, the existence, uniqueness theorem of the solution for INSFDEs is derived, and the estimate for the error between approximate solution and exact solution is given. On the other hand, under the linear growth condition, the uniform Lipschitz condition is replaced by the local Lipschitz condition, the existence, uniqueness theorem is also valid for INSFDEs on [t0,T]. Moreover, the existence, uniqueness theorem still holds on interval [t0,∞), where t0∈R is an arbitrary real number. 相似文献
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Existence and uniqueness of optimal solutions for multirate partial differential algebraic equations
The numerical simulation of electric circuits including multirate signals can be done by a model based on partial differential algebraic equations. In the case of frequency modulated signals, a local frequency function appears as a degree of freedom in the model. Thus the determination of a solution with a minimum amount of variation is feasible, which allows for resolving on relatively coarse grids. We prove the existence and uniqueness of the optimal solutions in the case of initial-boundary value problems as well as biperiodic boundary value problems. The minimisation problems are also investigated and interpreted in the context of optimal control. Furthermore, we construct a method of characteristics for the computation of optimal solutions in biperiodic problems. Numerical simulations of test examples are presented. 相似文献
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Fractional stochastic differential equations have gained considerable importance due to their application in various fields of science and engineering. This paper is concerned with the square-mean pseudo almost automorphic solutions for a class of fractional stochastic differential equations in a Hilbert space. The main objective of this paper is to establish the existence and uniqueness of square-mean pseudo almost automorphic mild solutions to a linear and semilinear case of these equations. A new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy. Finally, an example is provided to illustrate the obtained theory. 相似文献
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For a stochastic differential inclusion given in terms of current velocities (symmetric mean derivatives) on flat n-dimensional torus, we prove the existence of optimal solution minimizing a certain cost criterion. Then this result is applied to the problem of optimal control for equations with current velocities. 相似文献
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Thomas S. Angell 《Journal of Optimization Theory and Applications》1971,7(3):149-169
This paper extends some existence theorems of Cesari for optimal control problems to systems whose dynamics is described by functional differential equations of finitely-retarded type. We show that the proper choice of state space is the spaceE
1×C[–, 0], where >0 represents the time-lag of the system, and that it is necessary to choose initial conditions from a compact set inC[–, 0] as well as to employ the usual growth condition.This research was accomplished in the frame of research project AFOSR-942-65 at the University of Michigan. In particular, the author would like to thank Professor L. Cesari (University of Michigan) and Professor N. Chafee (Brown University) for many helpful remarks during the preparation of the research, which forms part of the author's doctoral dissertation written at the University of Michigan. 相似文献
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Existence and uniqueness of the mild solutions for stochastic differential equations for Hilbert valued stochastic processes are discussed, with the multiplicative noise term given by an integral with respect to a general compensated Poisson random measure. Parts of the results allow for coefficients which can depend on the entire past path of the solution process. In the Markov case Yosida approximations are also discussed, as well as continuous dependence on initial data, and coefficients. The case of coefficients that besides the dependence on the solution process have also an additional random dependence is also included in our treatment. All results are proven for processes with values in separable Hilbert spaces. Differentiable dependence on the initial condition is proven by adapting a method of S. Cerrai. 相似文献
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Stepanov-like pseudo almost periodic solutions for impulsive perturbed partial stochastic differential equations and its optimal control
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This paper is mainly concerned with the Stepanov-like pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of $p$-mean piecewise Stepanov-like pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under non-Lipschitz conditions. The results are obtained by using the fixed point techniques with fractional power arguments. Then the existence of optimal pairs of system governed by impulsive partial stochastic differential equations is also obtained. Finally, an example is provided to illustrate the developed theory. 相似文献
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Mark C. Veraar 《Journal of Evolution Equations》2010,10(1):85-127
In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: $({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.$ Here, ${(A(t))_{t\in [0,T]}}In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E:
(SE) {ll dU(t) = (A(t)U(t) +F(t,U(t))) dt + B(t,U(t)) dWH(t), t ? [0,T], U(0) = u0.({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right. 相似文献
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In this paper, we employ Malliavin calculus to derive a general stochastic maximum principle for stochastic partial differential equations with jumps under partial information. We apply this result to solve an optimal harvesting problem in the presence of partial information. Another application pertains to portfolio optimization under partial observation. 相似文献
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Nonstandard methods are used to give a simple construction of a solution to SDEs of the form , where are required only to be measurable, with, bounded. By working with an internal Brownian motion the proof avoids the complicated lifting and approximation arguments needed in previous existence proofs. 相似文献
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We consider a solution xt to a generic Markovian jump diffusion and show that for any t0>0 the law of xt0 has a C∞ density with respect to the Lebesgue measure under a uniform version of the Hörmander conditions. Unlike previous results in the area the result covers a class of infinite activity jump processes. The result is accomplished using carefully crafted refinements to the classical arguments used in proving the smoothness of density via Malliavin calculus. In particular, we provide a proof that the semimartingale inequality of J. Norris persists for discontinuous semimartingales when the jumps are small. 相似文献
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