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Stochastic differential games involving impulse controls and double-obstacle quasi-variational inequalities
Stochastic differential game Impulse control Quasi-variational inequality Viscosity solution
2012/6/25
We study a two-player zero-sum stochastic differential game with both players adopting impulse controls, on a finite time horizon. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) partial differential equati...
Geometric Influences II: Correlation Inequalities and Noise Sensitivity
Influences geometric influences noise sensitivity correlation between increasing sets Talagrand’s bound Gaussian measure isoperimetric inequality
2012/6/25
In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as ...
Harnack Inequalities for Functional SDEs with Multiplicative Noise and Applications
Harnack inequality functional solution delay SDE strong Feller property
2011/2/28
By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong...
Trace Inequalities with Applications to Orthogonal Regression and Matrix Nearness Problems
Trace inequalities stochastic matrices orthogonal regression matrix nearness problems
2010/4/16
Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where ...
Hadamard Product Versions of the Chebyshev and Kantorovich Inequalities
Chebyshev inequality Kantorovich inequality Hadamard product
2010/1/22
The purpose of this note is to prove Hadamard product versions of the Chebyshev and the Kantorovich inequalities for positive real numbers. We also prove a generalization of Fiedler's inequality.
Refinements of Inequalities Between the Sum of Squares and the Exponential of Sum of a Nonnegative Sequence
Inequality Exponential of sum Nonnegative sequence Normal random variable
2010/1/22
Using probability theory methods, the following sharp inequality is established: where , and for . Upon taking in the above inequality, the inequalities obtained in [F. Qi, Inequalities be...