Adaptive stochastic weak approximation of degenerate parabolic equations of Kolmogorov type
نویسندگان
چکیده
منابع مشابه
Adaptive stochastic weak approximation of degenerate parabolic equations of Kolmogorov type
Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...
متن کاملOn a class of degenerate parabolic equations of Kolmogorov type
We adapt the Levi’s parametrix method to prove existence, estimates and qualitative properties of a global fundamental solution to ultraparabolic partial differential equations of Kolmogorov type. Existence and uniqueness results for the Cauchy problem are also proved.
متن کاملAdaptive Weak Approximation of Stochastic Differential Equations
Adaptive time-stepping methods based on the Monte Carlo Euler method for weak approximation of Itô stochastic differential equations are developed. The main result is new expansions of the computational error, with computable leading-order term in a posteriori form, based on stochastic flows and discrete dual backward problems. The expansions lead to efficient and accurate computation of error ...
متن کاملConvergence Rates for Adaptive Weak Approximation of Stochastic Differential Equations
Convergence rates of adaptive algorithms for weak approximations of Itô stochastic differential equations are proved for the Monte Carlo Euler method. Two algorithms based either on optimal stochastic time steps or optimal deterministic time steps are studied. The analysis of their computational complexity combines the error expansions with a posteriori leading order term introduced in Szepessy...
متن کاملNull controllability of degenerate parabolic equations of Grushin and Kolmogorov type
The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator ∂ x + |x|∂ y (γ > 0) in the rectangle (x, y) ∈ (−1, 1)×(0, 1) or with the Kolmogorov-type operator v∂xf+∂ vf (γ ∈ {1, 2}) in the rectangle (x, v) ∈ T×(−1, 1), under an additive control supported in an open subset ω ...
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: Journal of Computational and Applied Mathematics
سال: 2010
ISSN: 0377-0427
DOI: 10.1016/j.cam.2009.12.011