General Linear Quadratic Optimal Stochastic Control Problem Driven by a Brownian Motion and a Poisson Random Martingale Measure with Random Coefficients
نویسنده
چکیده
Consider the minimization of the following quadratic functional J(u) = E ∫ T 0 [ 〈QtXt,Xt〉dt+ 〈Ntut, ut〉 ] dt+ E〈MXT ,XT 〉, where X is the strong solution to the linear state equation driven by a multidimensional Browinan motion W and a Poisson random martingale measure μ̃(dθ, dt) dXt = (AtXt +Btut)dt+ d ∑ i=1 (C tXt +D i tut)dW i t
منابع مشابه
Partial Information Linear Quadratic Control for Jump Diffusions
We study a stochastic control problem where the state process is described by a stochastic differential equation driven by a Brownian motion and a Poisson random measure, being affine in both the state and the control. The performance functional is quadratic in the state and the control. All the coefficients are allowed to be random and non-Markovian. Moreover, we may allow the control to be pr...
متن کاملEquivalence of stochastic equations and martingale problems
The fact that the solution of a martingale problem for a diffusion process gives a weak solution of the corresponding Itô equation is well-known since the original work of Stroock and Varadhan. The result is typically proved by constructing the driving Brownian motion from the solution of the martingale problem and perhaps an auxiliary Brownian motion. This constructive approach is much more ch...
متن کاملDynamic Programming for General Linear Quadratic Optimal Stochastic Control with Random Coefficients
We are concerned with the linear-quadratic optimal stochastic control problem where all the coefficients of the control system and the running weighting matrices in the cost functional are allowed to be predictable (but essentially bounded) processes and the terminal state-weighting matrix in the cost functional is allowed to be random. Under suitable conditions, we prove that the value field V...
متن کاملScaling limits for symmetric Itô-Lévy processes in random medium
Abstract We are concerned with scaling limits of the solutions to stochastic differential equations with stationary coefficients driven by Poisson random measures and Brownian motions. We state an annealed convergence theorem, in which the limit exhibits a diffusive or superdiffusive behavior, depending on the integrability properties of the Poisson random measure.
متن کاملAsymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise
Using key tools such as Itô’s formula for general semimartingales, Kunita’s moment estimates for Lévy-type stochastic integrals, and the exponential martingale inequality, we find conditions under which the solutions to the stochastic differential equations (SDEs) driven by Lévy noise are stable in probability, almost surely and moment exponentially stable. Keywords; stochastic differential equ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1102.3295 شماره
صفحات -
تاریخ انتشار 2011