Nonlinear Spdes: Colombeau Solutions and Pathwise Limits
نویسندگان
چکیده
منابع مشابه
Pathwise Taylor Expansions for Itô Random Fields
Abstract. In this paper we study the pathwise stochastic Taylor expansion, in the sense of our previous work [3], for a class of Itô-type random fields in which the di↵usion part is allowed to contain both the random field itself and its spatial derivatives. Random fields of such an “self-exciting” type particularly contains the fully nonlinear stochastic PDEs of curvature driven di↵usion, as w...
متن کاملPathwise Stationary Solutions of Stochastic Partial Differential Equations and Backward Doubly Stochastic Differential Equations on Infinite Horizon
The main purpose of this paper is to study the existence of stationary solution for stochastic partial differential equations. We establish a new connection between backward doubly stochastic differential equations on infinite time horizon and the stationary solution of the SPDEs. For this we study the existence of the solution of the associated BDSDEs on infinite time horizon and prove it is a...
متن کاملRough evolution equations
We show how to generalize Lyons’ rough paths theory in order to give a pathwise meaning to some non-linear infinite-dimensional evolution equations associated to an analytic semigroup and driven by an irregular noise. As an illustration, we apply the theory to a class of 1d SPDEs driven by a space-time fractional Brownian motion.
متن کاملAn Exact Connection between two Solvable SDEs and a Nonlinear Utility Stochastic PDE
Motivated by the work of Musiela and Zariphopoulou [24], we study the Itô random fields which are utility functions U(t, x) for any (ω, t). The main tool is the marginal utility Ux(t, x) and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate Ũ(t, y). Under regularity assumptions, we associate a SDE(μ, σ) and its adjoint SPDE(μ, σ) in divergence form whose Ux(t, x)...
متن کاملAn Exact Connection between Two Solvable SDEs and a Nonlinear Utility Stochastic PDE
Motivated by the work of Musiela and Zariphopoulou [24], we study the Itô random fields which are utility functions U(t, x) for any (ω, t). The main tool is the marginal utility Ux(t, x) and its inverse expressed as the opposite of the derivative of the Fenchel conjuguate Ũ(t, y). Under regularity assumptions, we associate a SDE(μ, σ) and its adjoint SPDE(μ, σ) in divergence form whose Ux(t, x)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998