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Difficulty: Hard
Category: Stochastic Calculus
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Topics: stochastic-calculus, euler-maruyama, convergence, sde
You are tasked with implementing the Euler-Maruyama method to simulate the solution of a stochastic differential equation (SDE). The SDE is given by: $dX_t = a(X_t, t) dt + b(X_t, t) dW_t$ where $W_t$ is a standard Brownian motion. You need to understand the convergence properties of the Euler-Maruyama scheme. What is the strong order of convergence of the Euler-Maruyama method?
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