Stochastic Process Analyzer

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X(t))dt + σdW(t)",   "parameters": {   "meanReversion": {   "type": "number",   "range": \[0.01, 10],   "default": 1,   "description": "Mean reversion speed (θ)"   },   "longTermMean": {   "type": "number",   "range": \[-100, 100],   "default": 0,   "description": "Long-term mean (μ)"   },   "volatility": {   "type": "number",   "range": \[0.01, 2.0],   "default": 0.2,   "description": "Volatility (σ)"   },   "initialValue": {   "type": "number",   "range": \[-100, 100],   "default": 0,   "description": "Initial value (X₀)"   }   },   "applications": \["interest-rates", "commodities", "volatility"],   "complexity": "medium",   "available": false   },   {   "name": "jump",   "fullName": "Jump Diffusion Process",   "description": "GBM with random jumps",   "equation": "dS(t) = μS(t)dt + σS(t)dW(t) + S(t-)dJ(t)",   "applications": \["crisis-modeling", "event-risk", "derivatives"],   "complexity": "high",   "available": false   },   {   "name": "heston",   "fullName": "Heston Stochastic Volatility",   "description": "Model with stochastic volatility",   "applications": \["options", "volatility-surface", "exotic-derivatives"],   "complexity": "high",   "available": false   }   ]   },   "authentication": {   "type": "api\_key",   "required": false,   "headerName": "X-API-Key",   "description": "Optional API key for rate limiting and analytics"   },   "rateLimit": {   "enabled": true,   "requests": 100,   "window": 3600,   "skipSuccessfulRequests": false,   "skipFailedRequests": true   },   "limits": {   "maxSimulationSteps": 10000,   "maxSimulationPaths": 10000,   "maxConcurrentRequests": 10,   "requestTimeout": 30000,   "maxPayloadSize": "10mb",   "maxExportSize": "50mb"   },   "logging": {   "level": "info",   "format": "combined",   "maxSize": "10mb",   "maxFiles": 5,   "destinations": \["console", "file", "rotating-file"]   },   "monitoring": {   "enabled": true,   "metrics": {   "requests": true,   "errors": true,   "performance": true,   "memory": true,   "cpu": true   },   "healthCheck": {   "path": "/health",   "interval": 30000,   "timeout": 5000   }   },   "cache": {   "enabled": true,   "type": "memory",   "ttl": 300000,   "maxSize": 100,   "redis": {   "host": "localhost",   "port": 6379,   "password": null,   "db": 0   }   },   "database": {   "type": "sqlite",   "path": "data/stochastic.db",   "options": {   "synchronous": "NORMAL",   "journal\_mode": "WAL"   },   "migrations": {   "enabled": true,   "path": "migrations/"   }   },   "security": {   "helmet": {   "contentSecurityPolicy": {   "directives": {   "defaultSrc": \["'self'"],   "styleSrc": \["'self'", "'unsafe-inline'", "https://cdnjs.cloudflare.com"],   "scriptSrc": \["'self'", "https://cdnjs.cloudflare.com"],   "imgSrc": \["'self'", "data:", "https:"]   }   }   },   "cors": {   "origin": \["http://localhost:3000", "https://claude.ai"],   "credentials": true,   "methods": \["GET", "POST", "PUT", "DELETE", "OPTIONS"],   "allowedHeaders": \["Content-Type", "Authorization", "X-MCP-Version", "X-API-Key"]   }   },   "features": {   "simulationBatching": true,   "componentCaching": true,   "exportFormats": \["json", "csv", "xml", "pdf"],   "realTimeUpdates": false,   "multiDimensional": true,   "customModels": false,   "distributedComputing": false   },   "integrations": {   "claude": {   "enabled": true,   "version": "4.0",   "endpoints": {   "completions": "https://api.anthropic.com/v1/completions"   }   },   "jupyter": {   "enabled": false,   "kernelPath": "/usr/local/share/jupyter/kernels/python3"   },   "r": {   "enabled": false,   "rscriptPath": "/usr/bin/Rscript"   }   },   "deployment": {   "environment": "development",   "containers": {   "docker": {   "image": "stochastic-mcp:latest",   "ports": \["3001:3001"],   "volumes": \["./data:/app/data", "./logs:/app/logs"],   "environment": {   "NODE\_ENV": "production",   "PORT": "3001",   "LOG\_LEVEL": "info"   }   }   },   "scaling": {   "minReplicas": 1,   "maxReplicas": 5,   "targetCPU": 70,   "targetMemory": 80   }   },   "documentation": {   "openapi": {   "enabled": true,   "path": "/docs/openapi.json",   "ui": "/docs"   },   "examples": {   "enabled": true,   "path": "/examples"   }   },   "testing": {   "enabled": true,   "coverage": {   "threshold": 80,   "reportFormats": \["text", "html", "json"]   },   "e2e": {   "enabled": false,   "browserless": false   }   },   "version": "2.0.0",   "lastUpdated": "2024-07-09T00:00:00Z",   "maintainer": {   "name": "Stochastic Process Analysis Team",   "email": "support@stochastic-mcp.com",   "url": "https://github.com/your-org/stochastic-process-mcp"   } }