Probability on Algebraic and Geometric Structures.

Cover -- Title page -- Contents -- Preface -- The fine structure of the stationary distribution for a simple Markov process -- 1. Introduction -- 2. Statement of results -- 3. Numerical estimates -- References -- Superdegenerate hypoelliptic differential operators -- 1. Salah Mohammed: A personal reminiscence -- 2. Hörmander's Theorem and the Malliavin calculus -- 3. Superdegenerate hypoelliptic operators -- 4. Proof of the theorem -- References -- Some remarks on the convolution equation * = and product semigroups -- 1. Introduction -- 2. Product Semigroups -- 3. Choquet-Deny Convolution Equation in General Semigroups -- References -- Limit distributions of products of I.I.D. random 2×2 stochastic matrices: an open problem -- 1. Introduction -- 2. Preliminaries -- 3. Discussion on the case 1/2&lt -- &lt -- 1 -- 4. Case when is the reciprocal of the golden ratio ( =(√5-1)/2) -- 5. Concluding Remarks -- References -- Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations -- 1. Introduction -- 2. Stochastic calculus via regularizations -- 3. Stochastic calculus via regularizations in Banach spaces -- 4. Kolmogorov path-dependent PDE -- References -- Matrices with zero row sums, tree theorems and a Markov chain on trees -- 1. Introduction -- 2. Some special ZRS matrices and the matrix -- 3. ZC1 and the theorem on the adjugate -- 4. Directed spanning trees -- 5. Graphs -- 6. Markov chains -- 7. Conclusion -- References -- Convolution of orbital measures on symmetric spaces: A survey -- 1. Introduction -- 2. Absolute continuity of the convolution of orbital measures -- 3. Properties of the density of the convolution of orbital measures -- 4. Symmetric spaces of Euclidean type -- References -- Exit times for some autoregressive processes with non-Gaussian noise distributions -- 1. Introduction.

2. An upper bound -- 3. Upper bounds for specific distributions -- 4. Lower bounds -- 5. A lower bound for Laplace distributed noise -- 6. Conclusions and comments -- References -- Brief history of optimal control theory and some recent developments -- 1. Introduction -- Energy conservation -- Element of arc -- Total time -- Functional -- Euler-Lagrange equation -- Legendre (1736-1813) -- Hamilton (1805-1865) - Weierstrass (1815-1897) -- Jacobi -- Bellman -- Question -- Pontryagin 1908-1988 -- Deterministic -- Stochastic -- 2. Optimal Control Theory adapted to Abrupt Financial Markets Changes -- Control problem with Markov regime switching with noise -- 3. Application -- 4. Conclusion -- References -- Krawtchouk matrices, Feynman path integral and the split quaternions -- 1. What are Krawtchouk matrices -- 2. Counting, controlled and erratic -- 3. What is quantum computing? -- 4. Ehrenfest Urn problem: Beyond Kac's solution -- 5. Topological interpretation of Krawtchouk matrices -- 6. Feynman sum over paths interpretation -- 7. Quaternions and related Lie groups and algebras -- Appendix A. Krawtchouk matrices -- Appendix B. Krawtchouk matrices from Hadamard matrices -- Appendix C. Pascal-Krawtchouk pyramid -- Appendix D. Subspaces of binary spaces -- References -- The Itô-Stratonovich formula for an operator of order four -- 1. Introduction -- 2. The Itô-Stratonovich formula -- 3. Dynamical system perturbed by a small operator of order four -- References -- Random walks on motion groups -- 1. Introduction -- 2. Motion group -- 3. Dynamic random walks -- 4. Concluding remarks -- References -- Existence, uniqueness, and energy of modified stochastic sine-Gordon equation with multiplicative noise on one-dimensional domain -- 1. Introduction -- 2. On Fourier Series Solutions -- 3. Existence and Uniqueness of Truncated Fourier Series _{ }.

4. Estimation of Expected Energy of Original System -- References -- Squared Bessel process with delay -- 1. Introduction -- 2. Construction of the Generalized Squared Bessel Process -- 3. The Stochastic Delay Differential Equation -- References -- Kravchuk matrices and induced operators on Clifford algebras -- 1. Introduction &amp -- Notational Preliminaries -- 2. Clifford Operator Calculus -- 3. Induced &amp -- Reduced Operators -- 4. Kravchuk Appell Decompositions of Clifford Algebras -- 5. Conclusion -- Acknowledgment -- References -- Back Cover.

This volume contains the proceedings of the International Research Conference "Probability on Algebraic and Geometric Structures", held from June 5-7, 2014, at Southern Illinois University, Carbondale, IL, celebrating the careers of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea. These proceedings include survey papers and new research on a variety of topics such as probability measures and the behavior of stochastic processes on groups, semigroups, and Clifford algebras; algebraic methods for analyzing Markov chains and products of random matrices; stochastic integrals and stochastic ordinary, partial, and functional differential equations.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.