thatboi
- 130
- 20
Hi all,
I am not familiar with stochastic processes, but I would like to know how to evaluate the following expectation value: $$\mathbb{E}[e^{\int_{0}^{t}d\tau(V_{i}(\tau)-V_{j}(\tau))}]$$ where ##\mathbb{E}[V_{i}(t)] = 0,\mathbb{E}[V_{i}(t),V_{j}(t')] = \gamma\delta_{ij}\delta(t-t')## for some constant ##\gamma##.
Any assistance is appreciated.
I am not familiar with stochastic processes, but I would like to know how to evaluate the following expectation value: $$\mathbb{E}[e^{\int_{0}^{t}d\tau(V_{i}(\tau)-V_{j}(\tau))}]$$ where ##\mathbb{E}[V_{i}(t)] = 0,\mathbb{E}[V_{i}(t),V_{j}(t')] = \gamma\delta_{ij}\delta(t-t')## for some constant ##\gamma##.
Any assistance is appreciated.