This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
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This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
MA 651
Stochastic Analysis
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This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
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This course introduces the fundamentals of stochastic calculus. Topics include probability measures and random variables; the Itô integral calculus; Itô's Lemma; Markov chains; random walks; the Wiener process; Brownian and geometric Brownian motion; filtrations; adaptive processes; Martingales and super-Martingales; the Martingale Stopping Time Theorem; Girsanov's Theorem and the Radon-Nikodym derivative; stochastic differential equations for single and multiple random processes; Kolmogorov equations and the Feynman-Kac Theorem. Applications include the modelling of continuous diffusion processes, and the development of solution techniques for stochastic differential equations. Topics may include stochastic optimization and jump processes.
Prerequisites: ST559 or equivalent.
Exclusions: MA451 or equivalent.
