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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Markov Chains and θ-Congruent Number Problem
马尔可夫链 θ-同余数 θ-全等数分布
2023/5/10
A positive integer n is called a θ-congruent number if n sin θ is the area of a triangle with rational side lengths and with an angle θ. Markov chains play a key role in the study of the distribution ...
A needle of length I dropped at random on a grid of parallel lines of distance
d apart can have multiple intersections if I > d. The distribution of the number
of intersections and approximate mom...
The Fastest Mixing Markov Process on a Graph and a Connection to a Maximum Variance Unfolding Problem
Markov connected graph edge tags transition rates
2015/7/8
We consider a Markov process on a connected graph, with edges labeled with transition rates between the adjacent vertices. The distribution of the Markov process converges to the uniform distribution ...
The Fighter Problem: Optimal Allocation of a Discrete Commodity
Bomber problem continuous ammunition discrete ammunition concavity
2011/9/20
Abstract: The Fighter problem with discrete ammunition is studied. An aircraft (fighter) equipped with $n$ anti-aircraft missiles is intercepted by enemy airplanes, the appearance of which follows a h...
Investment/consumption problem in illiquid markets with regimes switching
Optimal consumption liquidity effects regime-switching models viscosity solutions integro-differential system
2011/10/9
Abstract: We consider an illiquid financial market with different regimes modeled by a continuous-time finite-state Markov chain. The investor can trade a stock only at the discrete arrival times of a...
Computing hitting times via fluid approximation: application to the coupon collector problem
Computing hitting times fluid approximation coupon collector problem Probability
2011/9/14
Abstract: In this paper, we show how to use stochastic approximation to compute hitting time of a stochastic process, based on the study of the time for a fluid approximation of this process to be at ...
Moments of random sums and Robbins' problem of optimal stopping
Moments of random sums Robbins' problem Probability
2011/9/13
Abstract: Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value...
The secretary problem on an unknown poset
classical secretary problem maximal elements algorithm Combinatorics Probability
2011/8/26
Abstract: We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the num...
An extremal problem with applications to testing multivariate independence
boundary-value problem Green function multivariate indepen-dence asymptotic efficiency of test statistics
2011/1/18
Some problems of statistics can be reduced to extremal problems of minimiz-ing functionals of smooth functions defined on the cube [0, 1]m, m ≥ 2. In this paper, we study a class of extremal problems ...
Polygonal Homographic Orbits of the Curved n-Body Problem
Polygonal Homographic Orbits Curved n-Body Problem
2011/1/20
In the 2-dimensional n-body problem in spaces of constant curvature, 6= 0, with n ≥ 3, we study polygonal homographic solutions.
On the Imbedding Problem for Three-state Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues
imbedding problem three-state time homogeneousMarkov chains
2010/12/3
For an indecomposable 3×3 stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for tim...