The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

Kolmogorov Equation Associated to the Stochastic Reflection Problem on a Smooth Convex Set of a Hilbert Space

Here A :D(A) ⊂H →H is a self-adjoint operator, K = {x ∈H :g(x) ≤ 1}, where g :H → R is convex and of class C∞, NK(x) is the normal cone to K at x and W (t) is a cylindrical Wiener process in H (see Hypothesis 1.1 for more precise assumptions). Obviously the expression in (1.1) is formal and its precise meaning should be defined. When H is finite-dimensional a solution to (1.1) is a pair of cont...

Stochastic mortality models: an infinite-dimensional approach

Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvement...

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

On Stochastic Set Functions Ii

The Skorokhod Oblique Reflection Problem in a Convex Polyhedron

The Skorokhod oblique reflection problem is studied in the case of n-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to con...