ترغب بنشر مسار تعليمي؟ اضغط هنا

Exit problem as the generalized solution of Dirichlet problem

75   0   0.0 ( 0 )
 نشر من قبل Qingshuo Song
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod topology, which reveals the intrinsic connection between overfitting Dirichlet boundary and fine topology. As an application, we establish the sub and supersolutions for a class of non-stationary HJB (Hamilton-Jacobi-Bellman) equations with fractional Laplacian operator via Feynman-Kac functionals associated to $alpha$-stable processes, which help verify the solvability of the original HJB equation.



قيم البحث

اقرأ أيضاً

We reduce the construction of a weak solution of the Cauchy problem for the Navier-Stokes system to the construction of a solution to a stochastic problem. Namely, we construct diffusion processes which allow us to obtain a probabilistic representati on of a weak (in distributional sense) solution to the Cauchy problem for the Navier- Stokes system.
66 - E. Aurell , K. Sneppen 2001
We develop a framework to discuss stability of epigenetic states as first exit problems in dynamical systems with noise. We consider in particular the stability of the lysogenic state of the lambda prophage, which is known to exhibit exceptionally la rge stability. The formalism defines a quantative measure of robustness of inherited states. In contrast to Kramers well-known problem of escape from a potential well, the stability of inherited states in our formulation is not a numerically trivial problem. The most likely exit path does not go along a steepest decent of a potential -- there is no potential. Instead, such a path can be described as a zero-energy trajectory between two equilibria in an auxiliary classical mechanical system. Finding it is similar to e.g. computing heteroclinic orbits in celestial mechanics. The overall lesson of this study is that an examination of equilibria and their bifurcations with changing parameter values allow us to quantify both the stability and the robustness of particular states of a genetic control system.
88 - Xihao He , Xiaolu Tan , Jun Zou 2021
We study a principal-agent problem with one principal and multiple agents. The principal provides an exit contract which is identical to all agents, then each agent chooses her/his optimal exit time with the given contract. The principal looks for an optimal contract in order to maximize her/his reward value which depends on the agents choices. Under a technical monotone condition, and by using Bank-El Karouis representation of stochastic process, we are able to decouple the two optimization problems, and to reformulate the principals problem into an optimal control problem. The latter is also equivalent to an optimal multiple stopping problem and the existence of the optimal contract is obtained. We then show that the continuous time problem can be approximated by a sequence of discrete time ones, which would induce a natural numerical approximation method. We finally discuss the principal-agent problem if one restricts to the class of all Markovian and/or continuous contracts.
We formulate a Calabi-Yau type conjecture in generalized Kahler geometry, focusing on the case of nondegenerate Poisson structure. After defining natural Hamiltonian deformation spaces for generalized Kahler structures generalizing the notion of Kahl er class, we conjecture unique solvability of Gualtieris Calabi-Yau equation within this class. We establish the uniqueness, and moreover show that all such solutions are actually hyper-Kahler metrics. We furthermore establish a GIT framework for this problem, interpreting solutions of this equation as zeros of a moment map associated to a Hamiltonian action and finding a Kempf-Ness functional. Lastly we indicate the naturality of generalized Kahler-Ricci flow in this setting, showing that it evolves within the given Hamiltonian deformation class, and that the Kempf-Ness functional is monotone, so that the only possible fixed points for the flow are hyper-Kahler metrics. On a hyper-Kahler background, we establish global existence and weak convergence of the flow.
91 - Samuel Herrmann 2019
In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm so-called Walk on Moving Spheres was already introduced in the Brownian context. The aim is therefore to g eneralize this numerical approach to the Ornstein-Uhlenbeck process and to describe the efficiency of the method.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا