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Ross, Kevin - Department of Statistics, Stanford University
Random walk Convergence of scaled random walks
Stochastic Processes Stat219/Math136
Random vectors Characteristic function
Uniform integrability Convergence of expectations
Discrete time stopping times Optional stopping theorem
Definition of conditional expectation in L2 case IE(X|Y ), is the (a.s.) unique random variable which
Convergence in Lq Weak convergence
Kevin J. Ross Department of Statistics e-mail: kjross@stat.stanford.edu Stanford University
Continuous Time Stochastic Control Spring 2008
Discrete time Markov chains Transition probabilities
Definition of conditional expectation, general case IE(X|G), is the (a.s.) unique random variable which
Theory of Probability Place: Braun Lecture Hall, Mudd Chemistry Building
Martingale inequalities Martingale convergence theorem
SIAM J. CONTROL OPTIM. c 2007 Society for Industrial and Applied Mathematics Vol. 45, No. 6, pp. 21692206
Surface Patterning: Tool to Modulate Stem Cell Differentiation in an Adipose System
Continuous time martingales Right-continuous filtrations
Law (distribution) of a RV Almost sure convergence
A study of the free boundary of a two-dimensional singular stochastic control problem.
Stochastic Processes Amir Dembo (Revised by Kevin Ross)
Introduction Measurable space
Probability measure and probability space Random variables
Discrete time sub-and super-martingales Today's lecture: Sections 4.2
Definition and properties of expectation Integrability
Continuous time stopping times Optional stopping theorem
Doob decomposition (discrete time) Doob-Meyer decomposition (continuous time)
Continuous time Markov processes Transition probability functions
Counting process Poisson process
Branching processes Probability of extinction
Filtration Adapted process
Special Cases of CE Properties of CE
Brownian motion defined Existence of BM
Definition of stochastic process Sample paths
Math136 / Stat219 Course Goals Basic concepts and definitions of measure-theoretic
Reflection principle for BM Brownian hitting times
Stochastic Control in Continuous Time E-mail address: kjross@stat.stanford.edu