Convergence of symmetric Markov chains on ℤ^d

For each n let Y_t⁽ⁿ⁾ be a continuous time symmetric Markov chain with state space n^-1ℤ^d. Conditions in terms of the conductances are given for the convergence of the Y_t⁽ⁿ⁾t to a symmetric Markov process Y_t on ℝ^d. We have weak convergence of {Y_t⁽ⁿ⁾}: t ≤ t₀} for every t₀ and every starting point. The limit process Y has a continuous part and may also have jumps.