On Some Reachability Problems for Diffusion Processes
نویسندگان
چکیده
The main purpose of this paper is to discuss the minimization of energy spent in order that a controlled diffusion process reaches a given target, a d-dimensional bounded domain. The exterior Dirichlet problem for the Hamilton-Jacobi-Bellman equation is studied for a class of criteria which includes the case of energy. Extensions to diffusion with jumps, examples and some other reachability problems are considered.
منابع مشابه
Stochastic Reachability of Jump-Diffusion Process Using Sum Of Squares Optimization
This note uses sum of squares (SOS) relaxation to solve stochastic reachability problems for jump-diffusion processes. The main result is a polynomial characterization of the infinitesimal generator for the solution of a jump-diffusion process’ boundary value problem, thereby enabling one to compute a bound on the probability of reaching a target set in finite time using SOS optimization.
متن کاملSequential Monte Carlo simulation for the estimation of small reachability probabilities for stochastic hybrid systems
The problem of estimating the probability that a system reaches a given set within some time horizon is considered. Standard Monte Carlo methods for reachability probability estimation do not require specific assumptions on the system under consideration. However, they are computationally demanding when the probability to be estimated is small. An Interacting Particle System (IPS) approach has ...
متن کاملA Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملروش مسیر یابی ذره به منظور پیش بینی حرکت نفت در دریا
A two-dimensional two-phase numerical model is developed to predict transport and fate of oil slicks which resulted the concentration distribution of oil on the water surface. Two dimensional governing equation of fluid flow which consists mass and momentum conservation was solved using the finite difference method on the structured staggered grid system. The resulted algebric equations were so...
متن کاملReachability checking in complex and concurrent software systems using intelligent search methods
Software system verification is an efficient technique for ensuring the correctness of a software product, especially in safety-critical systems in which a small bug may have disastrous consequences. The goal of software verification is to ensure that the product fulfills the requirements. Studies show that the cost of finding and fixing errors in design time is less than finding and fixing the...
متن کامل