<p>The rapid growth and increasing popularity of cloud services have made effective resource management and energy consumption in data centers crucial. Virtual Machine (VM) consolidation is a widely adopted strategy to reduce energy consumption and minimize Service Level Agreement (SLA) violations. A key challenge in this process is the placement of VMs, which significantly impacts data center efficiency. Despite substantial progress in VM placement techniques, challenges remain, particularly in accurately identifying and managing underloaded and overloaded physical machines. To address these challenges, this paper proposes a novel stochastic process-based method for VM placement. The proposed approach uses a stochastic process-based prediction technique to estimate the probabilities of overload and underload in physical machines. By strategically placing VMs in machines that are predicted not to be underloaded or overloaded in the near future, our method optimizes resource allocation and reduces the frequency of migrations, energy consumption, and SLA violations. The effectiveness of the proposed method is validated using both the CloudSim simulator and the real-world PlanetLab dataset. Simulation results demonstrate that our approach outperforms existing methods in achieving a balance between energy efficiency and SLA compliance, while also minimizing VM migration overhead.</p>