The volume includes lecture notes and research papers by participants of the Seventh Symposium on Probability and Stochastic Processes held in Mexico City. The lecture notes introduce recent advances in stochastic calculus with respect to fractional Brownian motion, principles of large deviations and of minimum entropy concerning equilibrium prices in random economic systems, and give a complete and thorough survey of credit risk theory. The research papers cover areas such as financial markets, Gaussian processes, stochastic differential equations, stochastic integration, quantum dynamical semigroups, self-intersection local times, etc. Readers should have a basic background in probability theory, stochastic integration, and stochastic differential equations. The book is suitable for graduate students and research mathematicians interested in probability, stochastic processes, and risk theory.
Lecture notes: Stochastic integration with respect to fractional Brownian motion and applications by D. Nualart Entropy and economic equilibrium by E. Nummelin Credit risk-A survey by T. Schmidt and W. Stute Research papers: Optimal investment in incomplete financial markets with stochastic volatility by N. Castaneda-Leyva and D. Hernandez-Hernandez Price calculation for power exponential jump-diffusion models--A Hermite-series approach by M. Galea, J. Ma, and S. Torres Conditions for nonconservativity in quantum dynamical semigroups by J. C. Garcia and R. Quezada Some notes on a dependency measure by J. M. Gonzalez-Barrios An example of an averaged Markov decision process without stable policies by J. Gonzalez-Hernandez Closeness estimates for sums of independent random variables by E. Gordienko, M. Mendieta, and J. Ruiz de Chavez An example of infinite dimensional quasi-helix by C. Houdre and J. Villa A non-homogeneous wave equation driven by a Poisson process by J. A. Leon and M. Sarra Existence of self-intersection local time of the multitype Dawson-Watanabe superprocess by J. A. Lopez-Mimbela and J. Villa Levy processes in Banach spaces: Distributional properties and subordination by V. Perez-Abreu and A. Rocha-Arteaga Phase space path integral representation for the solution of a stochastic Schrodinger equation by L. A. Rincon A note on covariance characterization of some generalized Gaussian random fields by A. Talarczyk On two-parameter Stieltjes integrals for functions in Besov-Liouville spaces and stochastic integrals by C. Tudor.