557 research outputs found
Riemann-Liouville processes arising from Branching particle systems
It is proved in this paper that Riemann-Liouville processes can arise from
the temporal structures of the scaled occupation time fluctuation limits of the
site-dependent (d,\alpha,\sigma(x))branching particle systems in the case of
1=d<\alpha<2 and \int_{\R}\sigma(x)\d x<\infty.Comment: 12 page
Large and moderate deviations of weak record numbers in random walks
Record numbers are basic statistics in random walks, whose deviation
principles are not very clear so far. In this paper, the asymptotic
probabilities of large and moderate deviations for numbers of weak records in
right continuous or left continuous random walks are proved.Comment: 17 pages. arXiv admin note: substantial text overlap with
arXiv:1909.0976
Large and moderate deviations for record numbers in some non-nearest neighbor random walks
The deviation principles of record numbers in random walk models have not
been completely investigated, especially for the non-nearest neighbor cases. In
this paper, we derive the asymptotic probabilities of large and moderate
deviations for the number of "weak records"(or "ladder points") in two kinds of
one-dimensional non-nearest neighbor random walks. The proofs depend only on
the direct analysis of random walks. We illustrate that the traditional method
of analyzing the local time of Brownian motions, which is often adopted for the
simple random walks, may not be optimal for our cases.Comment: 15 Page
Minimax Weight Learning for Absorbing MDPs
Reinforcement learning policy evaluation problems are often modeled as finite
or discounted/averaged infinite-horizon MDPs. In this paper, we study
undiscounted off-policy policy evaluation for absorbing MDPs. Given the dataset
consisting of the i.i.d episodes with a given truncation level, we propose a
so-called MWLA algorithm to directly estimate the expected return via the
importance ratio of the state-action occupancy measure. The Mean Square Error
(MSE) bound for the MWLA method is investigated and the dependence of
statistical errors on the data size and the truncation level are analyzed. With
an episodic taxi environment, computational experiments illustrate the
performance of the MWLA algorithm.Comment: 36 pages, 9 figure
Non-conjugate boundary value problem of a third order differential equation
This paper is devoted to prove the existence of the optimal interval where the Green’s function is negative definite. The left and right endpoints of the interval are found. Then, a new principle of comparison of a third-order differential equation is established. As an application of our results, the solvability of a non-conjugate boundary value problem is discussed
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