Journal ArticleDOI
Adapted solution of a backward semilinear stochastic evolution equation
Ying Hu,Shige Peng +1 more
TLDR
In this article, an adapted pair of process with values in H and K and respectively is defined, which solves a semilinear stochastic evolution equation of the backward form: where A is the infinitesimal generators of a C 0-semigroup {eAt } on H.Abstract:
Let K and H be two separable Hilbert spaces and be a cylindrical Wiener process with values in K defined on a probability space denote its natural filtration. Given , we look for an adapted pair of process with values in H and respectively is defined in §1),which solves a semilinear stochastic evolution equation of the backward form: where A is the infinitesimal generators of a C 0-semigroup {eAt } on H. The precise meaning of the equation is A linearized version of that equation appears in infinite-dimensional stochastic optimal control theory as the equation satisfied by the adjoint process. We also give our results to the following backward stochastic partial differential equation:read more
Citations
More filters
Book
Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Journal ArticleDOI
Solution of forward-backward stochastic differential equations
Ying Hu,Shige Peng +1 more
TL;DR: In this paper, the existence and uniqueness of the solution to forward-backward stochastic differential equations without the nondegeneracy condition for the forward equation was studied under a certain "monotonicity" condition.
Journal ArticleDOI
Backward-Forward Stochastic Differential Equations
TL;DR: In this article, the authors show the existence and uniqueness of the solution of a backward stochastic differential equation with respect to the integrability of the terms involved in the equation.
Book ChapterDOI
BSDEs, weak convergence and homogenization of semilinear PDEs
TL;DR: In this paper, the theory of backward stochastic differential equations and its connection with solutions of semilinear second order partial differential equations of parabolic and elliptic type are presented.
Journal ArticleDOI
Nonlinear Kolmogorov equations in infinite dimensional spaces: the backward stochastic differential equations approach and applications to optimal control
TL;DR: Solutions of semilinear parabolic differential equations in infinite dimensional spaces are obtained by means of forward and backward infinite dimensional stochastic evolution equations in this paper, which reveals to be suitable also towards applications to optimal control.
References
More filters
Book
Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Markov Processes: Characterization and Convergence
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
Book
Stochastic integration and differential equations
TL;DR: In this article, the authors propose a method for general stochastic integration and local times, which they call Stochastic Differential Equations (SDEs), and expand the expansion of Filtrations.
Journal ArticleDOI
Adapted solution of a backward stochastic differential equation
TL;DR: In this paper, the authors considered the problem of finding an adapted pair of processes with values in Rd and Rd×k, respectively, which solves an equation of the form: x(t) + ∫ t 1 f(s, x(s), y(s)) ds + ∪ t 1 [g(m, x, s, g(m)) + y(m)] dW s = X.
Book
Stochastic Integration and Differential Equations : A New Approach
TL;DR: In this article, the authors present a rapid introduction to the modern semimartingale theory of stochastic integration and differential equations, without first having to treat the beautiful but highly technical "general theory of processes".