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Most papers published in this Special Issue of Mathematics are written by the participants of the XXXVI International Seminar on Stability Problems for Stochastic Models, 21­25 June, 2021, Petrozavodsk, Russia. The scope of the seminar embraces the following topics: Limit theorems and stability problems; Asymptotic theory of stochastic processes; Stable distributions and processes; Asymptotic statistics; Discrete probability models; Characterization of probability distributions; Insurance and financial mathematics; Applied statistics; Queueing theory; and other fields. This Special Issue contains 12 papers by specialists who represent 6 countries: Belarus, France, Hungary, India, Italy, and Russia.

Research & information: general --- Mathematics & science --- Probability & statistics --- inhomogeneous continuous-time Markov chain --- weak ergodicity --- rate of convergence --- sharp bounds --- differential inequalities --- forward Kolmogorov system --- prefetching --- optimization --- Markov decision processes --- random trees --- Galton–Watson --- capacitance --- dirichlet boundary value problem --- monte carlo method --- unbiased estimator --- von-neumann-ulam scheme --- network evolution --- random graph --- multi-type branching process --- continuous-time branching process --- 2- and 3-interactions --- Malthusian parameter --- Poisson process --- life-length --- extinction --- queuing system --- elastic traffic --- inpatient claim --- non-stationary intensity --- convergence analysis --- bounds on the rate of convergence --- wireless network --- file transfer --- daily traffic profile --- blocking probability --- continuous-time ehrenfest model --- first-passage time densities --- proportional intensity functions --- asymptotic behaviors --- multi-server queueing model --- rating --- self-sufficient servers --- self-checkout --- assistants --- multi-dimensional Markov chains --- retrial queue --- negative customers --- resource heterogeneous queue --- asymptotic analysis --- discrete time functional filter --- optimal unbiased estimation --- steady state --- equilibrium arrivals --- one-server queueing system --- orbit --- retrials --- limit theorem --- sum of independent random variables --- random sum --- asymptotic expansion --- asymptotic deficiency --- kurtosis --- parameter estimation --- gamma-exponential distribution --- mixed distributions --- generalized gamma distribution --- generalized beta distribution --- method of moments --- cumulants --- asymptotic normality --- inhomogeneous continuous-time Markov chain --- weak ergodicity --- rate of convergence --- sharp bounds --- differential inequalities --- forward Kolmogorov system --- prefetching --- optimization --- Markov decision processes --- random trees --- Galton–Watson --- capacitance --- dirichlet boundary value problem --- monte carlo method --- unbiased estimator --- von-neumann-ulam scheme --- network evolution --- random graph --- multi-type branching process --- continuous-time branching process --- 2- and 3-interactions --- Malthusian parameter --- Poisson process --- life-length --- extinction --- queuing system --- elastic traffic --- inpatient claim --- non-stationary intensity --- convergence analysis --- bounds on the rate of convergence --- wireless network --- file transfer --- daily traffic profile --- blocking probability --- continuous-time ehrenfest model --- first-passage time densities --- proportional intensity functions --- asymptotic behaviors --- multi-server queueing model --- rating --- self-sufficient servers --- self-checkout --- assistants --- multi-dimensional Markov chains --- retrial queue --- negative customers --- resource heterogeneous queue --- asymptotic analysis --- discrete time functional filter --- optimal unbiased estimation --- steady state --- equilibrium arrivals --- one-server queueing system --- orbit --- retrials --- limit theorem --- sum of independent random variables --- random sum --- asymptotic expansion --- asymptotic deficiency --- kurtosis --- parameter estimation --- gamma-exponential distribution --- mixed distributions --- generalized gamma distribution --- generalized beta distribution --- method of moments --- cumulants --- asymptotic normality

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Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise.Originally published in 1970.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Stationary processes --- Stationary processes. --- Stochastic processes --- 519.216 --- 519.216 Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Stochastic processes in general. Prediction theory. Stopping times. Martingales --- Bochner integral. --- Bochner's theorem. --- Bounded operator. --- Bounded variation. --- Brownian motion. --- Characteristic exponent. --- Characteristic function (probability theory). --- Complexification. --- Compound Poisson process. --- Computation. --- Conditional expectation. --- Continuous function (set theory). --- Continuous function. --- Continuous linear operator. --- Convergence of random variables. --- Coset. --- Covariance function. --- Cyclic subspace. --- Cylinder set. --- Degrees of freedom (statistics). --- Derivative. --- Differential equation. --- Dimension (vector space). --- Dirac delta function. --- Discrete spectrum. --- Distribution function. --- Dual space. --- Eigenfunction. --- Equation. --- Existential quantification. --- Exponential distribution. --- Exponential function. --- Finite difference. --- Fourier series. --- Fourier transform. --- Function (mathematics). --- Function space. --- Gaussian measure. --- Gaussian process. --- Harmonic analysis. --- Hermite polynomials. --- Hilbert space. --- Homeomorphism. --- Independence (probability theory). --- Independent and identically distributed random variables. --- Indicator function. --- Infinitesimal generator (stochastic processes). --- Integral equation. --- Isometry. --- Joint probability distribution. --- Langevin equation. --- Lebesgue measure. --- Lie algebra. --- Limit superior and limit inferior. --- Linear combination. --- Linear function. --- Linear interpolation. --- Linear subspace. --- Mean squared error. --- Measure (mathematics). --- Monotonic function. --- Normal distribution. --- Normal subgroup. --- Nuclear space. --- One-parameter group. --- Orthogonality. --- Orthogonalization. --- Parameter. --- Poisson point process. --- Polynomial. --- Probability distribution. --- Probability measure. --- Probability space. --- Probability. --- Projective linear group. --- Radon–Nikodym theorem. --- Random function. --- Random variable. --- Reproducing kernel Hilbert space. --- Self-adjoint operator. --- Self-adjoint. --- Semigroup. --- Shift operator. --- Special case. --- Stable process. --- Stationary process. --- Stochastic differential equation. --- Stochastic process. --- Stochastic. --- Subgroup. --- Summation. --- Symmetrization. --- Theorem. --- Transformation semigroup. --- Unitary operator. --- Unitary representation. --- Unitary transformation. --- Variance. --- White noise. --- Zero element.

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Mathematical models and computer simulations of complex social systems have become everyday tools in sociology. Yet until now, students had no up-to-date textbook from which to learn these techniques. Introduction to Mathematical Sociology fills this gap, providing undergraduates with a comprehensive, self-contained primer on the mathematical tools and applications that sociologists use to understand social behavior. Phillip Bonacich and Philip Lu cover all the essential mathematics, including linear algebra, graph theory, set theory, game theory, and probability. They show how to apply th

Mathematical sociology. --- Addition. --- Adjacency matrix. --- Advertising. --- Algorithm. --- Antisymmetric relation. --- Average path length. --- Balance theory. --- Betweenness centrality. --- Binomial distribution. --- Boolean algebra (structure). --- Calculation. --- Centrality. --- Circle graph. --- Clustering coefficient. --- Coefficient. --- Combination. --- Community structure. --- Complex network. --- Complexity. --- Computer simulation. --- Cooperative game. --- Defection. --- Demography. --- Diagram (category theory). --- Directed graph. --- Emergence. --- Employment agency. --- Employment. --- Epidemiology. --- Equivalence class. --- Equivalence relation. --- Expected value. --- Exponential distribution. --- Finding. --- General Social Survey. --- Graph theory. --- Grid network. --- Income. --- Independence (probability theory). --- Inequality (mathematics). --- Initial condition. --- Investor. --- Life expectancy. --- Main diagonal. --- Markov chain. --- Markov process. --- Markov property. --- Mathematica. --- Mathematical sociology. --- Mathematician. --- Mathematics. --- Matrix multiplication. --- Mutual exclusivity. --- Nash equilibrium. --- Natural number. --- Negative relationship. --- Normal distribution. --- PageRank. --- Parameter. --- Pareto distribution. --- Parity (mathematics). --- Percentage. --- Power law. --- Power set. --- Prediction. --- Preferential attachment. --- Prisoner's dilemma. --- Probability of success. --- Probability. --- Proportionality (mathematics). --- Quantity. --- Questionnaire. --- Random graph. --- Rational choice theory. --- Result. --- Sampling (statistics). --- Scale-free network. --- Scientist. --- Set theory. --- Simulation. --- Small-world network. --- Social class. --- Social movement. --- Social psychology. --- Social science. --- Sociology. --- Standard deviation. --- Statistic. --- Stochastic process. --- Subset. --- Summation. --- Symmetric matrix. --- Symmetric relation. --- Variable (mathematics). --- Venn diagram. --- Website. --- Wiring (development platform). --- Woman. --- Year. --- Zipf's law.

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"Credit risk is today one of the most intensely studied topics in quantitative finance. This book provides an introduction and overview for readers who seek an up-to-date reference to the central problems of the field and to the tools currently used to analyze them. The book is aimed at researchers and students in finance, at quantitative analysts in banks and other financial institutions, and at regulators interested in the modeling aspects of credit risk."--Jacket.

Credit --- Management. --- Adapted process. --- Arbitrage. --- Asset Sales. --- Asset. --- Bankruptcy. --- Barrier option. --- Basis Point. --- Binomial approximation. --- Binomial distribution. --- Bond (finance). --- Bond Yield. --- Bond valuation. --- Calculation. --- Call option. --- Capital structure. --- Comparative advantage. --- Convenience yield. --- Coupon (bond). --- Coupon. --- Credit (finance). --- Credit default swap. --- Credit derivative. --- Credit rating. --- Credit risk. --- Credit spread (options). --- Cumulative Dividend. --- Current liability. --- Debt Issue. --- Debt. --- Discount function. --- Discrete time and continuous time. --- Dividend payout ratio. --- Dividend. --- Equity value. --- Equivalent Martingale Measures. --- Estimation. --- Estimator. --- Exponential distribution. --- Fair value. --- Geometric Brownian motion. --- Government bond. --- High-yield debt. --- Implicit cost. --- Implied volatility. --- Information asymmetry. --- Interest rate swap. --- Interest rate. --- Issuer. --- Jump process. --- Latent variable. --- Least squares. --- Leverage (finance). --- Liability (financial accounting). --- Libor. --- Logistic regression. --- Market liquidity. --- Market value. --- Markov chain. --- Markov model. --- Mathematical finance. --- Merton Model. --- Moment-generating function. --- Money market. --- Option (finance). --- Par Yield Curve. --- Path dependence. --- Payment. --- Plain vanilla. --- Predictable process. --- Present value. --- Pricing. --- Probability of default. --- Probability. --- Put option. --- Random variable. --- Recapitalization. --- Repurchase agreement. --- Risk management. --- Risk premium. --- Risk-neutral measure. --- Semimartingale. --- Short rate. --- State variable. --- Swap (finance). --- Swap Curve. --- Swap rate. --- Swap spread. --- Synthetic CDO. --- Tax advantage. --- Tax shield. --- Tax. --- Trading strategy. --- Tranche. --- Underlying Security. --- Value (economics). --- Variance. --- Vasicek model. --- Yield curve. --- Yield spread. --- Zero-coupon bond.