Supersymmetric theory of stochastic dynamics

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Stochastic Calculus: Integrals and Processes

Explores stochastic calculus, emphasizing integrals, processes, martingales, and Brownian motion.

Mean Field Theory: Stochastic Analysis and Applications

Explores classical mean field theory, local interactions, and examples like individual-based SIR models and raindrop formation.

Stochastic Integration

Covers stochastic integration and exchange mobility for mathematics students.

Stochastic Integration: First Steps

Covers stochastic integration, process bracket, martingales, and variations in submartingales.

Stochastic Differential Equations

Explores Stochastic Differential Equations, discussing existence, uniqueness, Lipschitz properties, and explicit solutions.

Rigidity in Negative Curvature

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Effective Dynamics for Stochastic Differential Equations

Explores effective dynamics for non-reversible stochastic differential equations, covering molecular dynamics, bottlenecks, coarse-graining, and free-energy connection.

Nonlinear PDE Models with Stochastic Fractional Perturbation

Explores nonlinear PDE models with stochastic fractional perturbation, focusing on regularity identification and space-time noise interpretation.

Martingales and Stochastic Integration

Covers martingales, stochastic integration, and localizing processes using stopping times.

System Variables and Types of Systems

Covers system variables, types of systems, and process control in static and dynamic systems.