Refactor SDE simulation parameters for clarity and correctness

- Replaced hardcoded drift and diffusion calculations with defined parameters for better readability.
- Updated the Euler-Maruyama implementation to use the new parameters, enhancing maintainability.
- Added array indexing access to the state concept for improved usability in simulations.

Author: WenyinWei

examples/parallelism_usage_demo.cpp

@@ -203,22 +203,15 @@ void demonstrate_monte_carlo_simulation() {
             std::mt19937 rng(i);  // Seed with simulation index
             std::normal_distribution<double> normal(0.0, 1.0);
 
-            // Create SDE system
-            auto drift = [](double t, const std::vector<double>& x, std::vector<double>& fx) {
-                double mu = 0.05;
-                fx[0] = mu * x[0];
-            };
-            
-            auto diffusion = [](double t, const std::vector<double>& x, std::vector<double>& gx) {
-                double sigma = 0.2;
-                gx[0] = sigma * x[0];
-            };
+            // Define SDE parameters
+            const double mu = 0.05;    // drift coefficient
+            const double sigma = 0.2;  // volatility coefficient
 
             // Simple Euler-Maruyama implementation
             std::vector<double> state = {initial_price};
             for (double t = 0.0; t < t_final; t += dt) {
                 double dW = normal(rng) * std::sqrt(dt);
-                state[0] += 0.05 * state[0] * dt + 0.2 * state[0] * dW;
+                state[0] += mu * state[0] * dt + sigma * state[0] * dW;
             }
 
             final_prices[i] = state[0];

examples/state_concept_usage.cpp

@@ -64,6 +64,10 @@ int main() {
         auto begin() const { return data.begin(); }
         auto end() const { return data.end(); }
 
+        // Add array indexing access required by system_state concept
+        double& operator[](std::size_t index) { return data[index]; }
+        const double& operator[](std::size_t index) const { return data[index]; }
+        
         const std::string& get_name() const { return name; }
     };