Diffusion Approximation of Non-Markovian Processes
نویسندگان
چکیده
منابع مشابه
Non-Markovian Quantum State Diffusion
A nonlinear stochastic Schrödinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unravelling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including...
متن کاملSimulating non-Markovian stochastic processes.
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical and efficient algorithm like the Gillespie algorithm for Markovian processes, with the difference being that now the occurrence rates of the events depend on the time elapsed since the event las...
متن کاملExploiting non-Markovian Bio-Processes
The Stochastic Simulation Algorithm (SSA) is a milestone in the realm of stochastic modeling of biological systems, as it inspires all the current algorithms for stochastic simulation. Essentially, the SSA shows that under certain hypothesis the time to the next occurrence of a biochemical reaction is a random variable following a negative exponential distribution. Unfortunately, the hypothesis...
متن کاملStochastic Impulse Control of Non-Markovian Processes
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of combined optimal stochastic and impulse control of a fairly general class of diffusions with random coefficients. Unlike, in the Markovian framework, we cannot a...
متن کاملAnalysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation
The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). In this work, an explicit finite-difference scheme for TFDE is presented. Discrete models of a non-Markovian random walk are generate for simulating random variables whose spatial probability density evolves...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1975
ISSN: 0091-1798
DOI: 10.1214/aop/1176996408